with tennis grips the over grips aren't close to as durable as a replacement grip but a replacement grip is probably close to 1/8 of an inch thick and usually have sticky tape on the entire backside that would leave marks if u ever took it off, other than looking funny and maybe too big to fit back in your case they'd be great
i've never put 1 on a cue i like no wrap but for over grips what-a-grip would work the best, they're nice grips but they're stretched when put on and once u get 1 lil hole/tear in it the grip is done
if u sweat really bad and nothing else works i'd check out a gamma hi tech grip, slightly sticky/tacky they're very nice and durable but you'd have to put it on right and deal with the thickness of it even though it's a thinner type of replacement grip