Will doing muscle ups one side at a time put an unhealthy amount of strain on the shoulder that comes up first? It feels like that might be the case. My original plan was to get to being able to do 10 muscle ups in a row and then work on my technique. Now it looks like it’ll be getting 1 muscle up with perfectly strict form and then working up to more reps?
One handed muscle ups?!
No, if I could do one handed muscle ups I’d probably have the level of body control required to be a gold medallist gymnast :P. I mean like propping my left arm onto the bar first and then the right arm (- YouTube).
1 arm at a time is a bad idea. It is dangerous and could also make a habit out of incorrect technique. Do the muscle ups fresh with plenty of rest until they become easy. I would encourage starting with a couple of training sessions with a gymnastics coach. I do like the guys advice to do chest level pull-ups as prep. I would move to kipping muscle-ups as the next progression and then try the full version after a couple of weeks with kipping. You can also do holds in the tough positions and slow negatives after kipping muscle-ups.
I got a slight to moderate pec tear doing a sloppy muscle up 1 arm at a time (by accident). I had already completed a workout and was fatigued so I had no business being on the bar but I think 1 arm at a time is risky even when fresh.