It is so hard when they fight the sleepiness!! lol
Charlotte hated being wrapped from day dot. She also slept better on her tummy. To begin with though, although she was younger than your bub, I wrapped her bottom half only. Perhaps if you start by only wrapping him from the chest down, so his arms are free. Also have you got 2 dummies? One for his mouth and one for his hand? It may keep him from pulling the other one out...?
also have you got a teddy or a tag blanket or something else you start giving him only when it is sleep time, so that he associates that item with sleep, allowing you to eventually stop wrapping or removing he dummy without distressing him. I found that helped Charlotte a lot too.