An option I use to prevent contaminating the solvent, and to make it easy to put exactly the amount of solvent I want, right where I want it is to buy some solvent transfer pipettes.
These are plastic bulbs with a long tube spout.
You can buy them from a lab supply house or from Brownell's under the Accur-Bore solvent.
I fill the bulb with solvent, put the patch or brush into the chamber or bore, then give it a squirt of solvent. No waste, no mess, and no contamination.