David, I see you are asking about a half stock gun, yes that's fine to do it without a cap for a Tennessee rifle.
Not all of those southern half stock rifles were originally made as half stock guns, some were full stock guns that were cut back or the forends broke up and were shortened. You see all kinds of stuff, no cap and no entry pipe, wood under ribs with the pipes pinned to the rib, flat metal plate at the end of the forestock in place of a cap, etc. There's a lot you can do that could be considered "correct".