I do not get how としてしまう is used in the following sentence. If the meaning ofとして = as, for; not even and しまう = to finish doing (something), what do they mean together? (assuming I have split the phrase correctly).
男性がイラッ!! としてしまう!? [女性の言いがちワード]
This is not the として meaning as/for, but a simple conjugation of the する verb イラッとする, meaning "to feel annoyed". In addition, the しまう here isn't being used in the sense of "finish doing", but rather the more common sense where it indicates the preceding verb is an unfortunate occurrence.
So 男性がイラッ!!としてしまう!? as a whole means "Guys will feel annoyed?!"
Incidentally, this sentence is loosely linked to the following phrase in the style of a relative clause, so the whole thing could be translated as if it was one sentence:
This would mean "Words girls tend to say that make guys feel annoyed".