Sure, you could put a in-line filter containing a water-absorbent, but then your absorb would weigh more through the trip. At least you could throw it away between trip, or depending on absorbent type and packaging, potentially regenerate it in the oven.
But I'd suggest you let a "self-inflater" self inflate as much as possible. And only top if off with breath.
To get any moisture back out, take other opportunities to fill it with cold air but empty it when its warm. At home, in the winter, that's easy. Let it fill outside, let it warm inside and then squeeze the warm, more humid air out. But even while BPing, you could let it fill with cool air but deflate after it's been in the sun for a while and warmed up. Wash, rinse, repeat.