Hamlet wants revenge for his father's murder. If he kills Claudius at the moment he's praying, Hamlet thinks, Claudius's soul will be pure and he'll be forgiven, and can therefore get into Heaven. King Hamlet died without a final confession/absolution/sacrament etc. and so his soul is wandering in Limbo. (I think that's the correct theological interpretation, but feel free to correct me if I have the doctrine wrong.)
I think that cringe means that a response to embarrasement. But right now in this text I think this word means that they didn't want that to happen. Or they thought that was not good. Hopefully it's right. I mean that's just my opinion. :D
