The NVMe can stay put, the cooler, well that's anotehr story. So long as the parts that are protruding from the motherboard aren't gong to impeded your installation or worse, break off when given some force, then you need to disassemble them, to make sure you don't have to waste money on something that could've easily been avoided.
Novice's shouldn't risk it. Experts make mistakes as well but they try and make sure they aren't ruining perfectly good hardware especially since the pandemic has made things worse...or if you're Linus who wants to ruin things for the sake of "YT content".
My vote, is SSD, leave. Cooler, take it off.