Instead of buying a squeegee you could make on for free or very little. (First instructable, please comment)
Step 1: Supplies
Step 2: Cutting
Using your xacto knife, cut a piece of tubing about six inches longer than your barrel. then, cut 2 square holes close to the end 180 degrees apart. Next cut a 8x8 piece of t-shirt. You also need some thin wire. I got mine from an old speaker wire.
Step 3: Wrapping
Get the center of your t-shirt piece and lay it next to the tube. Next, put your wire through the hole and wrap it around the cloth several times.
Step 4: Duct tape
Tape around the wire so it will not scratch your barrel.
Step 5: Cleaning
Run the squeegee through your barrel several times to clean it.