My "apocalypse skill" is 'doctor.'
I have reference material and basic equipment. It turns out that, without modern diagnostics and access to the industrial pharmacopia, doctoring becomes fairly simple. You have no way to diagnose many conditions, and no way to deal with them anyway.
I had considered 'brewer', with a focus on distillation, but the equipment would be a hassle.
'Powder maker' would be the third one. As in, black powder. The process of making potassium nitrate from basic materials is stinky and disgusting, but on the other hand, it helps deal with sanitation problems.