As mentioned earlier, 'can you be over licenced?' .... Probably Not.
(Exception if true: - I have read here somewhere, someone said that 'under licenced' was less of a fine than under permitted with a CDL - can't remember the thread - towing heavy trailer or something)
Question is, even if your state does NOT require a CDL, it will be a DMV (read expert) or a senior/DoT certified officer that says 'No'... HOWEVER, when you get pulled over by the local LEO, chased down for not pulling into a weigh station, or questioned by whoever attends an accident you're involved in, chances are ignorance of the LEO will cause a whole load of wasted time or grief if he thinks you should have one. Standing on the side of the road to argue your point untill you can proove you don't need one isn't the way I'd want to go. You'd be making him seem ignorant/foolish or whatever...
So, my money is with getting your CDL eventually, regardless of need.
.... "Actually Sir, it's not commercial AND historic so no CDL, BUT just to keep you happy.." (producing CDL) "nerr ne nerr ne nar narrrr".