No if the computer can't do the manual countdown, no self-destruct. Can't do things manually
Yeah the whole Trek security is pretty awful in Deadlock, you see them avoiding cover, walking straight to the enemy and getting shot etc.
The reset button in Star Trek Voyager was a very common complaint. Nothing has consequences beyond the episode. No matter what happens, everything is forgotten the episode. Ship get damaged, repaired offscreen next episode. The Doctor undergoes a life-altering traumatic experience. Forgotten the next episode and never mentioned ever again.