My BP cartridge hunting loads are usually made with nitro cards and old Felton Blue Streak wads with waxed edges. These are a very hard felt. I usually do not shoot enough rounds to worry about fouling.
I shoot a lot BP skeet with nitro cards and plain Celotex wads and do not remember any smoking wads laying on the field. I supposed it could happen. If I am shooting a lot of BP skeet I will spray water down the barrels to soften the fouling and cool the barrels.
For muzzle loading skeet I use soft felt wads soaked it moose milk because I will be shooting a lot an I will be shooting rather quickly after loading.
For ML hunting I use peanut oil on Celotex wdas or as mentioned, I will not use any cushion wad which tends to tighten the pattern.
Good Luck.
