On the assumption that the Q400 stick pusher is similar to the Q300 pusher (someone can confirm if this is the case), if he doesn't want the stick pusher, i.e., he believes it's activated in error, he doesn't need to fight it, he can de-power the stick pusher with a button on the glare shield, or have the PNF do it.
It's been a while, but I'm positive the Q400 also has a stick pusher cutout pushbutton on the glareshield.
Whilst you raise a fair point about being able to use the cutout, I'm not convinced that in the likely circumstances at play here, that doing so would have achieved anything more beneficial.
Unlike a situation flagged up by a system problem, where the cutout pushbutton is used as part of a checklist procedure, where the stick pusher suddenly fires and catches the crew unaware, it is completely natural to use force to override it as a first instinct.
I would be fairly certain that the Colgan crew were not expecting or prepared for the stick pusher. Add to that a presumably dark night, and equally likely a dark cockpit, combined with that horrible moment of "what the ****?" and you have a situation where asking either pilot to go fishing about trying to hit a small pushbutton on a badly illuminated glareshield is not a great option.
I don't know what the panel illumination was like on the 300, but on the 400 it was extremely poor. Even at max illumination, the overhead panel in particular was almost unreadable, and I would assume that the Colgan crew had no additional illumination (such as storm lighting or dome lights) to assist with an instantaneous identification of glareshield pushbuttons. Remember, this is a pushbutton that most pilots will never use outside of the simulator, and so there is no 'muscle memory' associated with finding it in the same way as the every day selections on the panel.
It is also worth considering as one of those hindsight issues, that had this been done (a non-standard, non-checklist, unbriefed action), what view would the investigating authorities take if there had still been an accident, but with some survivors? I'm not convinced they wouldn't try to find a way of hanging the crew out to dry.