Should be fine. After EVERY hunt I run a Boresnake through whatever rifle I used that hunt. I bought a snake for every caliber in my 3 dozen+ arsenal (including shotguns as well). If the day included rain, fog, snow etc I'll put a few drops of CLP on the "knot" of the snake where the rope meets the mop. If the weather outside is below 40ish I'll let the rifle warm to room temp & then run a snake in it & wipe the outside off to prevent/remove condensation.
I've shot Barnes bullets for over 2 decades & I'm sure "technically" my rifles are "copper fouled" but they are hunting guns, not paper punchers but I've never "stripped or defouled" the bores. I just keep powder residue & moisture out of them before sticking them back in the safes.