Most coolers fit the socket that the CPU goes into, so if yo ure using the same socket the same cooler should fit. Secondly, does the CPU you are buying come with a cooler already in the box? new CPUs should come packaged with a stock cooler.
Personally, as a cooler for a CPU is just a heatsink and a fan, I wouldn't see the harm in running the same cooler that came stock for that socket. I would try looking up some images of the stock cooler for that new processor though, and make sure the one you have is relatively the same size.