There are numerous medications with dry mouth/throat as a side effect. Timing is everything: If I need those, I arrange my dosing schedule so that a paying gig or formal choral performance occurs shortly before a dose rather than promptly after. That might mean being bone dry during a sound check last-minute rehearsal, but then a swig of water doesn't affect the flow of the show. I'm much less fussy for social singing occasionas when opportunities to drink are plenty. Formal choral situations I've experienced don't allow water on stage, so for example Handel's Messiah usually means at least a solid hour without refreshment. Pre-hydration and dose timing mean everything in such situations.

But sometimes I miss the mark in one way or another and have to do a gig feeling far from my best. One technique that helps is good breathing: If your throat is wide, wide open for inhaling you get maximum air volume entering with minimum contacting the throat surface. (It also means maximum lung filling in minimum time.) A pinched, narrow throat dries much faster because more of the air makes contact with the surface to absorb moisture.

In emergency dryness I have a couple of methods to stimulate salivation: One is to pinch lightly on the side of my tongue with my teeth, the other to bend my tongue way-y-y back hard as I can. These can be worked into pregnant pauses in patter, between verses or during applause, and are easily hidden by a smile. In fact if I'm singing too soon after an allergy pill, either method works far better than water, which has too little viscosity to adhere to throat and vocal folds. If I did have access to water in such a situation, I'd first drink to replenish my salivary glands, then get the saliva going (to drink water afterwards just washes it away).

I haven't tried slippery elm but I've heard it's good for mucous membranes; I've heard the same about comfrey but since I'm no herbalist, that's pure gossip.