(you haven't mentioned what powder you choose to use)

I use an emptied spray bottle that once housed eyeglass cleaner. In it I put
2oz - 71% isoprophyl alcohol
1oz - Ballistol.... (any water soluble gun oil can be used)

I am assuming your powder-of-choice is not Blackhorn209). Oddly enough, I have met a few different Blackhorn 209 users with traditional smokepoles over the years at nearby gun ranges.
The bore-swabbing recommendations for that powder is different.

Blackhorn 209 powder is not a good fit for sidelocks, Even the hottest ignition caps (along with nipple priming) cannot be trusted.