I'd like to buy some large, washable cutlery-sized spoons with a
water-repellent coating; i.e. if you dip it in water, it comes out
dry, like wax paper. Maybe Teflon or a non-stick coating would work?
Not lab spoons or cooking utensils, but something that you could eat
with.

Does such a thing exist? Where? :)

I must say I've never heard of such a thing. Have you tried waxing a
spoon? And have you tried eating soup with it?