I just tried it and couldn't cancel by right-clicking. Gives me an idea, though...
Maybe make it so you can click the power off, if you get a detrimental card... but when it expires, you automatically draw one of the better cards? That would incentivize players to keep a bad draw in anticipation of getting a good one when it wears off. Just a thought! Might be a lot of work to develop something like that, though.
Since I started playing again last year, I've used Secondary Mutation hundreds of times, and I have yet to get a single monkeymode. It used to happen all the time, at the worst times! I was starting to think they'd removed the effect, or made the chance even lower. At this point, I'm going to cheer when monkeymode happens again, because it's been so long... even if it immediately results in my death.