fans get a lot more bent out of shape about player reputations than players do, so it wouldn't surprise me if Bertuzzi had a lot of friends in the NHL. Heatley was pretty universally liked by players across the league and for whatever reason almost all you'd read about on here was what a dickbag he is.
Cooke, on the other hand, IIRC has had some things said about him by players that would lead you to believe he's not liked. He is, however, good at hockey. He has a "gutless" reputation for a reason, though, and that is because he almost always ducks on-ice attempts at holding him accountable for his play. I'd say always against bottom six players, and almost always against skilled players. I think he'd be willing to take a beating in the right circumstances, but it'd have to be something the other team would be crazy to consider...like one of their skilled guys willing to sit for 5 minutes just to pummel him. I doubt very much he'd accept a challenge from Bordy or McLeod. Iggy though...Interesting, and I can see both Iggy initiating, to set the tone for his tenure with the Avs as a veteran leader and Cooke accepting just because the tradeoff in penalty minutes is so one-sided. Even then it'd have to be in the right circumstances. Avs ahead, probably.
Booing gets old, and while it might affect some guys Cooke has to be in the top % as far as time spent being booed in the NHL. I don't think he'll notice. Maybe yell "you suck!" every time he coughs up the puck or misses a hit or whatever. I've always thought booing marginal players (if that is indeed how you view him) was counterproductive--it's more likely to give them an inflated sense of self-worth than depress them if it's coming from the opposition.