If you have absolutely no options, you could use DFHack's 'slayrace undead' command [...]
Damnit. Getting the feeling that my initial estimation of being screwed was right.

Ok then, before I resort to cheating I might as well play the joker card: SEND IN THE MINERS!
Now concerning the miner-civilian-uniform / miner on military duty problem, I only see one real solution:
* Take out the mining labour on both miners -> wait until they dropped the picks -> assign them to squad -> equip them with picks -> wait until they pick up the picks again -> slay zombie!
Would that work? Or is that "can't use the same picks for military"-problem actually referring to specific picks, so as if those picks get tagged as "civilian picks" forever?
if that solution shouldn't work for technical reasons:
Is there any way to trick those miners into "accidently bumping into" the zombie while they are carrying their picks?
I mean as regular civilians they would normally run away from the zombie right? But often enough a civilian still doesn't make it in time or whatever happens there when they get involved in wild brawl with something ... how I love those fights some wild animals pick with my woodcutters getting busted as a consequence. There must be some way to arrange such an event with my miners and the zombie?