Try a tampon, they are excellent at absorbing paint and the fluff cleans the barrel real clean, only adaption you need to make is attaching longer string to pull through.
Also you can get different absorbing strengths depending on amount of paint.
Playtex® Slimfits® Tampons
Playtex Slimfits Tampons have the slimmest plastic applicator, so they're comfortable to fit and insert even if it's your first time using a tampon on a marker.
Playtex® Gentle Glide® Tampons
Playtex Gentle Glide Tampons have a unique design that adjusts to custom-fit your marker, and their smooth plastic applicator provides comfortable insertion.
Playtex® Silk Glide® Tampons
Playtex Silk Glide Tampons have a silky smooth cardboard applicator that is easy to insert and easy to dispose of - just flush and that's it!
Playtex® Portables® Tampons
Playtex Portables Tampons are plastic applicator tampons that come in a discreet, convenient carry size. Put one in your marker case. Or your pocket. No one will ever know - it's protection on the go!