Welcome to the community, and congrats on the new Green Cheek! He/She is an adorable little Yellow-Sided!
I'm assuming that either Fish is either an adult who wasn't handled much or that got much attention at his/her first home, or you got Fish as a parent-raised baby. Either way, the fact that you've gotten Fish so far with hands already in just a couple of weeks is excellent progress; weeks are like seconds in parrot-time, and it literally takes many people who bring home a non-tame bird months and months to years just to get their birds to take a treat from their hand through the cage bars! So you guys are doing great!
I myself would not go backwards and all of a sudden start using a perch/dowel, since he's already eating from your hands and getting closer and closer to accepting your fingers to step-up on. However, you're correct, you certainly do not want to accidentally "encourage" or "reward" Fish when he bites you. Green Cheeks have a tendency to be a bit nippy, even ones that are completely hand-tame, cuddly, snuggly, etc. (trust me, I speak from experience, my Bowie is not over 2 years old and I got him as a hand-raised/hand-fed baby from a private breeder at 12 weeks old, and even though he's my baby and loves nothing more than to snuggle in bed and get head-scratches, back scratches, etc., he also loves to let me know when he's "annoyed", lol).
Green Cheek's are very much "velcro birds", meaning that they love attention and love, and absolutely HATE being ignored; they also become extremely jealous when "their person/people" pay any attention to other birds in the house, and in my experience Bowie also hates it when I pet the dogs! So in my experience, the absolutely best way to stop a Green Cheek from biting/nipping is by using the "Shunning" Method...How the "Shunning Method" works is very simple and straightforward, and it usually works most of the time as long as every person in the house uses it every single time the bird bites/nips; if everyone in the house that handles the bird is not on-board with using the Shunning Method every time the bird bites, then that's when the bird gets mixed-signals, and can also start to play favorites with the one person who doesn't ignore them when they become nippy...Basically all you do with the Shunning Method is every single time Fish bites/nips at all, you immediately say a phrase that you choose and that you say to him every time he bites/nips, and all people need to say the same phrase, and say it firmly and with authority, but never want to yell or scream it at him, or act like you're mad at him, because negative-reinforcement does not work with parrots...So basically every time that Fish purposely bites or nips anyone in the house, they immediately say the phrase firmly to him, for example a good phrase that is simple and to the point is "No Bites!", and then the person immediately puts Fish down, and I've found that the best place to put then is right down on the floor where you're at with him, because they hate being on the floor, lower than you. Some people put their birds back on their cages or play-stands, but to me that sends mixed-signals, because I don't want to associate their cages with a negative experience, nor do I want to put the bird down onto a fun area, like their play-stands, gyms, etc. So putting them down right on the floor where you're at works perfectly. Then after you put him down on the floor, you immediately turn your back to him, literally, just turn your back to him, and totally ignore him in every way for about 5 minutes. If he starts talking to you, crying, chirping, whining, whatever, you don't respond to him at all, you don't even look at him, never make eye contact with him, you need to act like he doesn't exist. When I put Bowie down on the floor he starts yelling "My Baby! My Baby! Gimme Kisses!", which obviously tears at my heartstrings, the little jerk! But you have to stay strong...I usually walk into a different room and pretend like he doesn't exist, don't say a word to him, don't even look his way. Sometimes he flies to me after I put him down, and if that happens, say he lands on my shoulder, I don't say anything to him at all, I simply put him right back down on the floor again, and this needs to last for a full 5 minutes, no less, but no more either because if you do it for too long a time he'll lose interest and the purpose gets lost...If you do this every single time he bites, even if he does it immediately again after the first 5 minutes is up, you have to do it again, every single time he bites/nips, eventually he'll get the idea; usually it doesn't take long at all (unless he's using his beak to climb-up onto your hand or shoulder, etc., that's not a bite, although bite-pressure training is another technique that you can look into as well)
Now, because this is happening WHILE you're trying to train him to step-up, I understand things can get confusing because you don't want to accidentally reward him if he happens to step-up and then bites you! Basically the way I would handle this is that if he steps-up onto your finger you immediately need to praise the hell out of him and reward him with his favorite treat, it should be automatic the second he steps-up or does whatever it is you're trying to train him to do...However, if you're trying to get him to step-up and he starts to step-up and then bites you, you still need to give him the "No Bites!" and put him down on the floor immediately, because you're absolutely correct, if you just reward him for stepping-up even though he also bit/nipped you, all he's going to see is that "When I bite them I get treats!". They always remember getting the treat or the praise, and if you reward him for stepping-up and totally ignore the fact that he bit you right after he stepped-up on your finger, then you're are essentially rewarding him biting you, which is a huge no-no. Again, you need to keep in-mind that they always remember getting the treat, and if the last thing he did before you gave him the treat was he bit/nipped you, then to him you're rewarding the bite/nip, not the stepping-up.
And again, I would not at all start using a dowel, perch, etc. to teach him to step-up, as this is actually known to cause a whole other set of possible issues and unwanted behaviors, I won't go into that right now, but just know that you were correct in thinking that using a dowel/perch to teach him to step-up in order to prevent him from biting is totally counterproductive, because you're not only teaching him to step-up onto a perch instead of your finger, but you're also not doing a thing to try to teach him not to bite/nip; you can actually kill two birds with one stone (wow, that's bad) if you train him to step-up directly onto your finger, and then also train him to not bite using the Shunning Method at the same time if he happens to bite you while he's stepping up.
***Again, just as the others above have mentioned, this is just another method of training, there are many, and it's simply what has worked for me to both eliminate the constant nipping, and at the same time still be able to teach him to step-up. There are many different training methods out there that you're going to hear, and none of them are "wrong", as each bird is an individual and different methods work for different birds. So it might just be a matter of trying different methods until you see one working, but make sure you give each individual training method enough time to be able to tell if it's going to work....(And when I said that "no training method is wrong, it's just a matter of finding out which works for your individual bird", I should have elaborated that there are training methods that are definitely "wrong", and they are the ones that use any type of Negative-Reinforcement in order to elicit a response...and of course you can never, ever, ever smack or spank your bird, or the really popular "hit/tap/flick the bird's beak when he bites", i don't know why people think that this is a good option, but all that this will do is succeed in making your bird terrified of you. They are not dogs or cats, they are much more intelligent and think on a much higher level than dogs and cats do...
