If you want to stop swaddling him, then you just don't swaddle him.
Next, ALL babies, WILL play with their hands or chew/suck on them, or have a 'startle reflex.' It is a normal and natural developmental thing that babies do & grow out of as they get older. They also need to explore their hands and move them around because it is all a part of natural development, and part of their reflexes etc.
Not all babies "have to" be swaddled.
It is also NORMAL that a baby "play" before falling asleep.... it is their way of "winding-down" before actually passing out. Much like how some adults have to read before going to bed, in order to relax. I doubt if any adult actually closes their eyes and passes out to sleep as soon as their head hits their pillow. Same thing with a baby.
In fact, I think its GOOD that your baby seems to be able to amuse himself before falling asleep. This shows he can "self-soothe." Which is good. Some babies dont' know how to do that. Yours does. That's good.
BOTH my kids, before they actually fell asleep, would "play" and babble to themselves in the crib too and amuse themselves. I was PROUD of them. It is good. Then eventually, they would fall asleep all on their own. Which is good. Each baby, falls asleep in their own way. THey do not have to all be swaddled in order to fall asleep... unless you want a baby that completely does not move around. But eventually, all babies, NEED to be out of the swaddle.... and their motor skills and reflexes will occur. You can't stop them from moving or playing with their hands. Its a good thing he is doing that... because it shows he is developing normally.
He is a young baby... and to me, he has his own way of falling asleep... and self-soothing. It does not mean that he has a "hard time" falling asleep just because he is playing with his hand. It means he is good at self-soothing and is self-reliant and CAN. Which not all babies can do.
Your baby is doing great, to me. He does not have to be in a swaddle.
All the best,
Susan