While I admire your willingness to help out this parrot, I have to agree that re-homing pets that you already have taken responsibility for because you want to bring the new bird home isn't the correct solution to your dilemma. That's not fair to your cats, nor is it a good sign that you're ready to take-on another pet that will live for decades. My concerns too go to what happens when another new pet comes along for you to take-in, but you don't think it's going to work well with your current parrot? Do you then re-home just like the cats? You see why this isn't a good solution to your problem, I'm sure...
The question you need to be asking the experienced members of this forum is "What precautions must I take in my home in order to safely welcome a new parrot into my house with my current 2 cats?" That is a proper question that many people on this forum can answer because they have years of experience dealing with the exact same issue.
It's true that cats are natural hunters and killers, and no matter how sweet they are or whether or not they have hunted or killed another animal/bird in the past, or whether or not they are de-clawed, etc., none of this makes any difference at all because their hunting/killing instincts are innate and cannot be removed with time nor tameness. This being said, can you have both a parrot and a cat living in the same home without incident? The answer to this is a resounding "yes", but ONLY if you make rules and procedures for your home, and EVERY PERSON living in the home commits to always following those rules and procedures. You cannot have your parrot out of the cage while the cats are free in the room, nor can you allow your cats to torment the parrot while it's inside it's cage as they tend to do. Cats love to sit and stare at their future prey, and forcing a parrot to sit inside it's cage while a cat or cats sit outside of the cage making them nervous can cause such stress that the bird start to self-mutilate. But, if you are willing to re-home your 2 cats then you can't care much about moving them to a separate room with a latching door whenever the parrot is out. That being said, you still must ask yourself some questions that have nothing to do with your 2 cats really:
-Are you able to give the parrot at least 4-5 hours, at a minimum, out of his cage every single day and interact with him, while the cats are shut in a separate room
-Are you willing to locate the parrot's cage in the "main room" of your house where the people in your house spend most of their time when they're home, such as the living room, den, family room, TV room, etc.? You cannot locate a parrot's cage in a spare bedroom or a room off away from where the "action" of your house is, where the parrot can hear people but not see them. And saying this, you must ask yourself the question "How will this effect the mental well-being of my 2 current cats?"
-Are you ready to take-on the responsibility of adding another pet to your home that has the intelligence of a human toddler, and as such needs the same type of attention and stimulation? How will this effect your cats and their welfare?
-I hate to add this question but it begs to be asked, "If you are so willing and ready to rehome your current 2 pets, how will your attitude towards this new parrot change over time as well?" Parrots are constantly, and I mean constantly re-homed from one owner to another to another to another, far more often than dogs, cats, reptiles, etc. are, and this is because people get a cute, tame, hand-raised baby parrot that is 12-23 weeks old, love it, and then it suddenly shows it's intelligence, it's attitude, it's personality, and it's individual characteristics, just as a human being does, and the original owners don't like the mess the bird is creating, don't like the attitude of the bird, which may include nips and bites, don't like the screaming and the noises of displeasure the parrot starts to make when the owner moves him to a back bedroom out of frustration, and finally the first owner says "Hell with this, I can make some money selling the parrot, his cage, and all of his stuff", and they re-home him to home #2. Home #2 does the same, as does home #3, #4, and so-on, until either the bird dies from malnutrition, self-mutilation, or even physical abuse, OR someone with parrot experience comes along and is willing to commit the time, energy, MONEY, etc. that it takes in order to earn a parrot's trust, then spend hours every day re-training, or simply training the parrot, and forming a close bond with the parrot. So you must ask yourself if you are this person, or not in it for the long-haul...
-Do you have the financial capability and access to a Certified Avian Vet nearby in order to keep the parrot healthy, and if need be, get him advanced Avian medical care that is often necessary when they get sick or injured? The specialist vet bills from a Certified Avian Vet can easily exceed $1,000 just for one initial visit with the necessary cultures and swabs, blood work, x-rays, and medications it often takes to diagnose a parrot's illness and treat it. It's not like taking a dog in to get it's shots or be spayed/neutered. Not even close. And you cannot rely on home-remedies as a lot of people try to do when their parrots become sick with an infection, parasite, or other illness, as the poor bird's in these situations always pass away after a long battle with the illness. And the reason that these parrot owners refuse to take their sick parrot's to the Avian Vet isn't usually because they don't care or wouldn't love to, but rather because they cannot afford $500-$1,000 a-pop to take them and treat them.
These are just a handful of the questions that anyone and everyone needs to ask themselves BEFORE, well before they decide to bring a parrot into their home and their family, whether it's a young, hand-raised, baby parrot right from it's breeder, or it's an adult parrot who has had at least one prior home before. Birds are not the same as bringing home a cat or a dog, or a reptile or a rodent, they are of a higher intelligence, and they have personalities very similar to that of human beings. They let you know when they are happy, but also when they are not happy. You can lose their trust and then face such a stressful, trying time in your home that you end-up not being able to deal with them anymore.
***I suggest that just as an education for yourself before you make a decision about bringing this parrot home, that you jump onto your local Craigslist, change the search result radius to 200 miles, the max on Craigslist, and then type "parrot" into the search bar, and count the number of pet birds that need new homes within that small, 200 mile radius of your home, and read the reasons that the owners list for rehoming them. I'm willing to bet that the #1 reason people list for having to re-home their pet bird's (we can safely just assume that most people aren't going to just come out and say that the bird has a "behavior issue", or so they think, lol), is because "We just haven't had enough time to spend with him/her, and he/she spends most all of their time in their cage, without any interaction from us", or something of the sort. And that isn't a false statement at all, but it's only a small piece of the puzzle as to why they are re-homing them...