Z is not a great hockey fighter for a few reasons.
1.) His size is a disadvantage for fighting on skates. It's a matter of center of gravity. The lower the center of gravity, the easier it is to maintain balance.
2.) It is not a huge component of his game. The guy is a Norris Trophy winner and three time finalist. I doubt it is something he works on in the off season. A guy like Shawn Thornton takes boxing classes during the summer. Chara bikes the Tour de France route and climbs Mt. Kilimanjaro.
3.) His father wrestled in the Olympics for Czechoslovakia. Stories about his development have always reported that wrestling with his dad was a large part of his training growing up. So he will probably always default to a wrestler's mentality.
4.) His main weapon seems to be a haymaker, which like his slapper is hard to get off in real conditions. But if he does land a clean one, with his size and leverage, I wouldn't want to be behind on the receiving end.
5.) I don't think he is a willing fighter, especially now. When he was younger he had to fight because he was the biggest guy out there and players are always trying to prove themselves (especially in the WHL). Then when he got the NHL, there was the same mentality, BUT also his skating took forever to develop. So if he wanted to play in this league he had to fight some to get minutes. But now he picks his fights based more on necessity (ie The Captain stepping in to handle a situation) rather than because guys are challenging him all the time.
6.) Though I will say, knowing what we know about Chara's work ethic, if he felt that fighting was the only way for him to stay an NHL player, he'd work hard to make himself the best in the league.