He is adorable!
I have just been put in a similar situation as you when a tiny little black kitten turned up at my back door about 7 weeks ago. He was trying to steal food from the bowl I put out for my ex-neighbours large ginger and white cat (long story). He had absolutely no fear of the neighbours cat or of my large long haired male cat Widget but he was terrified of humans. I guessed from that behaviour he was probably feral. He was in such a skinny state and his fur was in very bad condition so I decided, feral or not I needed to get him into the house and feed him, get him checked over by the vet and see if I could get him into a better condition.
Well to cut a long story short, I had vowed I would get him happy, healthy and vet treated and then re-home him, as my elderly arthritic cat, Widget, really didn't need a bouncy annoying kitten living with him. Well as I said that was over 7 weeks ago and I have fallen madly in love with Alfie (as I named him) and he has been integrated with my cat Widget. I'd be lying to say there weren't any spats along the way or that they are best buddies, but they are getting on. Widget, being so much bigger than Alfie, can just give him a bit of a slap and that usually stops Alfie from being too bouncy around him, but I also make sure Widget can have peaceful quiet moments on his own by closing Alfie into the sitting room at night and by giving Widget , Widget only spaces in the house where Alfie can't get to due to cat flaps, so Widget can get away from Alfie if he wishes.
Alfie has brought a bit of a spark back to Widget, as if having a bit of a young whipper snapper around has reminded him how to play and that life doesn't all have to be about eating sleeping and asking for pain killers for his aches. He still gets his pain killers when he feels bad, but it seems to be less often than usual. I think chasing Alfie has done him a lot of good.
I'm telling you all this just because if you do feel you would like to keep him, maybe try integration with your wobbly legged oldie, as it just might work out for you. I'm a strong believer that cats choose us, not the other way around, and it sounds to me like you were meant to find this pretty little boy. As long as your older cat has safe places to get away from this bouncy boy and you keep a careful eye on them until you are sure they have established boundaries you could find that the wee one puts a new spring into the oldies wobble.
Good luck whatever you decide is right for all concerned.
