I would hate to fully swaddle him and take away that soothing technique, but he's definitely young to be able to control them. I think you could either try to swaddle so that his hands are up by his face and he can suck on them but his arms don't go flailing, or seeing as he's so young, you could help hold his hand there while you shh/pat or something similar (in the hopes that he settles faster) and then gradually reduce your help as he gets older and gains more control over his limbs.
As for letting him be, at his age I would probably leave him to settle on his own no more than 10min or so. I'd rather set up good, long sleeps with shh/pat or picking him up to calm him than let him fuss and squirm and get OT. Do you think he's struggling with gas at all? It sounds like it could be a factor with his behavior. You could also try tweaking your wind down a bit to see if that helps.