with my DS2 I gave up on wrapping at about 2 weeks old cause he'd get out of it while sleeping and wanted to starfish sleep with his arms. Instead I've got him in a sleeping bag so he's warm overnight.
It might take a bit (a few days or so) for him to get used to not having the wrap on but he will get used to it. I know my DS (about 2 1/2 mths now) will sleep for about that length of time for about half his day naps (usually naps on a lambskin or in his bouncer) and sleeps longer at night in the bassinet. He's only in the sleeping bag at night.

Grobag is one label for sleeping bags. I currently have DS2 in a homemade 2nd hand one with sleeves and my mum made a couple more for him as I don't have the smaller sized ones as I swapped DS1 over to sleeping bags sometime after 6 mths and I scored a number of secondhand grobags off ebay for him.