RG59 and RG6

My condo was built in 1978.    Its hard to tell if its 6 or 59 unless I poke a hole in the wall to find out.  If  it's RG59, and I would want to redo some connectors, will a RG6 stripper and connector  be compatable with RG59 coming out of the wall?  I only plan on using RG6 of course if I ever do in home upgrades.  I could probably pay Cox to run new coax from the tap but I'm trying to avoid that if possible.  The condo is very picky where cables are run and holes are drilled.