I lied. This choice isn't important at all. There's nothing here but horrible death.
Interestingly, though, there are two different ways to die. The previous 'dead man walking' choice, the quip to make before using the booby-trapped grease gun, was completely meaningless, but here we can pick our poison.
If we make a fuss, this happens:
If, on the other hand, we play it cool, this happens: