You don't need to buy anything special for cleaning. A piece of fishing line with a loop tied in the end or a piece of line trimmer cord with a slit in it near the end will work just fine as a pull through. Simply pull a few patches through until they come out clean. Ballistol is a good cleaner, but alcohol will be adequate if you don't have anything better. Basically you just don't want to use anything that will degrade the seals or detonate, but with a break barrel the only seal you really have to worry about is the o-ring at the breach.
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