How about Champion?
Legs' name has changed to Hima, but Legs is still a nickname. Hima is the name of a sassy baby who crawls everywhere and gets into trouble all the time in a show we watch.

seemed like a fitting name. Hubbs was a hold out until 1 scene in an episode when the mom sets Hima down saying "Here's 2 baskets of toys, will this keep you busy for 10 minutes so I can start dinner" or something like that. Our Hima is always behaving juuust long enough that we start to get distracted, then she makes a beeline for whatever she isn't supposed to mess with: books, half made bird toys, plastic, floor candy, Alex McGrumperton, you know: whatever's around.

troublemaker.
Yeah, Hima is coming up on a year old and is doing great! She has a cage setup with her mobility in mind, and we still are giving her water out of a bottle cap a couple times a day, but she could probably be trusted with a small dish at this point. When she gets into Alex's cage she was doing fine with his old water dish: a small hook-on dish.
They really do adapt well. Hima is a completely unique individual, and we are completely devoted to her sassy self. A one legged budgie would probably be more mobile than Hima, but then again maybe not. She uses her legs and beak all together, and when she wants to boyyyy she can really haul around with speed. Gets around well enough to be stubborn about wanting to sit on my chest, climbing instantly back wherever I put her lol. She does have a "uniquely Hima" problem of getting poo in odd places. We have found it in her armpits, and the other day she had a "cheekspot" that wasn't. Eew. Still gotta get or make her a budgie diaper. With a 1 legger, I don't think that would be something you would have to deal with, but IDK.
Can you take a video of the little one moving around? I'd be curious to see how the little one gets around.
Do you have any food items he/she can get to easily? I'd probably go with tons of spray millet, and soaked pellets and cooked foods I think. That old I don't think I would try to formula feed, but I don't think I would leave the little one with just hard adult food. Will the siblings feed the little one? Hima's parents also didn't do the best job of feeding her thru to weaning, and her first molt was nothing but stress banded feathers dropping.