OP, others will disagree, but I use Hoppes for my first clean on a swab after 20 strokes with JB Non Embedding Bore Paste. ..ten strokes, then another ten with Hoppes on another swab...then repeat that process with Ballistol. Then repeat with clean swabs or patches.
Some will tell you that Hoppes contains harmful acids. I don't know if it does or doesnt, but I figger if it works in a powder burner, it shouldn't hurt my air rifles, especially after the Ballistol rinse.
I won't argue the point, but everyone has to do what feels right to them.