Depends somewhat on where you live and if it gets below freezing. Is this an outside wall? Running pipes on the inside has advantages - less likely to freeze and then split. Running copper through existing studs is not really feasible for a long run...but you could use PEX, which is flexible and could be threaded there. PEX is generally not affected by freezing (doesn't mean flow won't be stopped), but any connectors that freeze are fair game and could split.