Would d20 be the best system to handle it? I don't know. Some rambling thoughts:
I think it would be fun to have a system with disadvantages like "takes time showboating", "easily distracted by managers", "long hair easy to pull", etc.
Going a point buy route you could make very desirable 'feats' attainable from the get-go but make them expensive, such as "frequently no-sells", "will not submit" (think classic Undertaker, you gotta knock him out or pin him) or a finisher that can be applied out of nowhere and/or applied on opponents much heavier than yourself (I was involved in a wrestling e-fed a few years ago and nobody would take a finisher that didn't meet those requirements. I also saw a ton of 6 foot 7, "technically skilled brawlers" because that was seen as a min-max combo that could do anything - everybody had some kind of power bomb but no one used it as a finisher, hmmm).
Recreating the ebb and flow of an old-school wrestling match is something I've never quite gotten from a video game. What could an RPG do to model this better? One thing about wrestling is that no matter how many bone-crushing moves the first wrestler strings together on the second from the opening bell, you still gotta give both wrestlers long turns on both offense and defense. Some kind of 'momentum reserve points' system might be in order to model these turnarounds, I don't know how it would work. Something like if you take the "attack before the bell" advantage and get a good roll, you take points off your victim's vitality but give up 'momentum reserve points' the victim can play later when he wants to take a turn on offense. Otherwise they'll always be trying to attack each other before the bell.
Charisma would not be a dump stat in the game, that's for sure. Intelligence could help you get more technical moves and counter-moves, while Wisdom would be about 'ring savvy' like knowing when to move out of the way so the charging opponent slams into the turnbuckle instead of you.