Hi my baby girl only has one leg because she was attacked by an animal.
When I treat her I just put her in a small cage with all the poles removed and pad it with a soft cloth or confetti. This will limit his movement and help the wound heal better.
And when my babegirl lost one lag, she likes to sleep on her stomach, so you need to prepare a platform not more poles to help him. Also causes some issues, her butt feathers get dirty with poo while she sleeps, so you need to wash his bum everyday (lol) I tried cutting her butt feathers short, that would work , but it seems not too good.
About biting casts, you can try cutting a small Elizabethan collar (like a neck drag, usually used for sick cats or dogs) with sponge or thick paper (tape the edges to prevent injury), this will prevent the budgie from biting itself. (Always observe the skin on his neck for injuries) I haven't used this method, but from the examples of other budgie moms in my budgie network group, it works.
I am a chinese budgie mom, so my english is not good, I hope you can understand.
There maybe other professional questions to ask your vet. Hope your baby gets well soon.