Does this have to be a strictly non-magical type class, like fighter or rogue, or can it have spell-like abilities like a monk? Because without eventually gaining some innate ability to disable or ignore freedom of movement effects, the class will end up quite useless at higher levels.
As the wrestler advances in levels, it'd be cool to let him enlarge himself X times/day, to help his grapple mod. Although in RL, having leverage helps a lot, and it's easier to get that levarage if you're short (and built like a dwarf). Oh well.
I think the class should also be adept at tripping (imp trip at some point), as well as grapping. It should be a good general tactic to take someone down, then try to pin them. Also, perhaps allowing the wrestler to retain his dodge bonuses against other opponents, at a max amount that increases with char. level (sort of like armors' max dex bonus restriction). And of course, they should be able to inflict lethal damage with their grapples if they choose, albeit not as much as monk.
As for class skills, maybe: escape artist(?), tumble, concentration(?), jump, bluff(?), craft (everyone has it), intimidate(?), perform (even if authentic (not pro) wresting, it's still a sport, and thus entertainment). Eh, on second thought just copy the monk's skill list, it's close enough.