My phone works fine in the rain. The
touchscreen is garbage, because it can't differentiate my finger from a puddle on the screen. Granted, there are pressure sensitive touchscreens out there. If you want a good map that you can take notes on, you'll need a custom app. In my experience, writing on screens is very fussy business. So you might be able to a custom app, custom hardware, maybe spending thousands per unit.
But, paper. I mentioned a brand name. It's wonderful stuff, nothing like the paper you're thinking of. This solution costs a few bucks per person.
https://www.riteintherain.com/
Edit: this "rain" crap is a digression from the "fire" problem. I don't have experience there, but I imagine "the electric infrastructure and cell towers burnt down" is more of an issue... again, paper and pencil wins.