I did some more research, and it appears that the small alcohol wipes like you see at the doctors will provide a flame that will last a minute or 2 using flint and steel.
I'm also looking into the small foil pouches of white petroleum jelly to use for fire gel. Again, I think medical supply stores will carry these as well.
You wouldn't have to pre-smear your cotton with it, and could be stored without smearing everything else or having their own container.