The lack of antiperspirants on Chinese shop shelves can be a problem.

True.
Chinese people are by and large less hairy than westerners. Deoderants are therefore not in demand.
Many of the menfolk needn't shave, the lucky blighters, and armpit hair is rare, for both sexes.
I've bought cheap perfume, and spray it onto my armpits. It works okay for about a day at a time.
BTW, I'm touched that you will pray for our resident padre. It's a pity he won't recognize your kind gesture in public. Still, you've tried your best to make peace with him. You couldn't have done more!