Hi CR,
This is what I do whether wet wading or bringing along my waders.

Wearing waders while hiking in or keeping in bag?

While I wouldn't carry both my wet wading and dry wading gear at the same time, this shows that it will all fit into a small 20L day pack.

Contents: Waders ( Size LL ), Dry Socks, Neoprene ( wet ) wading sock, wading boots ( size 13's ), 13 gallon trash bags, paper towels and externally there are two 24 oz. insulated water bottles. Even when loaded like this, there is still ample room for snacks, etc.

These little packs can be had for around $15 and the only thing I do to them is shoot them twice with waterproofing spray. This doesn't make them waterproof, just helps to keep the water rolling off this ducks back in a light rain.

I also wear a fishing fanny pack but am not opposed to just carrying one box of flies, a spare leader, tippet and nippers, etc. in my shirts box pockets