Although yes, if one freaks out, they all might, I've actually found the birds much more willing to come back if at least one of them is comfortable coming to me.
Even though its easier to work with a single clipped bird than it is to work with two flighted birds together, I honestly don't find it that much more difficult doing so as long as you stick with positive interactions and allowing the birds the choice. Yes, it requires "work" figuring out ways to work with a terrified bird that wont hold still, but IMO, it's better than forcing a bird to be with you simply because they can't get away.
To each their own, of course.
2budgies, birds often do better away from their cage because you take them away from the only secure place they know and to an area where they feel insecure and vulnerable. I've come to learn that sometimes it's best working with birds in their comfort zone rather than out of it, because if you work with them out of their comfort zone, you may have training issues while back in their comfort zone. If you work with them in their comfort zone first, they may respond better once out of their comfort zone, after they are already comfortable with you.
I used to train in that matter, but have since changed how I work with my birds. I don't know if you'd be interested in trying different ways to work with them, but I hope you are able to earn their trust and they become excellent companions!