You can’t use the standard YouTube app because it requires you to have a linked Nintendo account and connect to Nintendo, which on CFW would lead to a ban.
However, there is a modded version of YouTube floating around which has been tweaked to allow use on CFW. Sorry, you will have to do some googling for that one.
I feel like this rests in the gray area of conversation. However, if I crossed the line, mods, please delete If you must.