I don't pan lube. Though if you have a tapered bullet pan lubing is necessary. Unless you have a Pope style pump with a tapered die. I'll use a slightly oversized sizer die and wipe the base on a rag. A sizer die the same diameter as dropped or .001 bigger works great. I know it's not what you asked except for wiping on a rag. A little rubbing alcohol on a shop rag leaves the base clean.

plastic window screen with  a piece of thin cloth under it on your table...works great !  Just cuts off the lube but doesnt scratch bullet.......I didnt patent it so your all welcome to it.......

I dip lube instead of pan lubing, and it has the same problem with lube on the base.

I put a large sheet of freezer paper on the workbench as I lube, and wipe the base clean on the paper.  Then, set the bullets aside to cool slightly before inserting into the cases.  Inserting in the cases scrapes off excess lube, and I wipe the residue off with my finger, returning it to the can I dip out of by scraping it off on the edge.  When I get a large area covered with the base smears, I scrape it off with a putty knife and return it to the melt can.

After I'm done inserting all the bullets, I wipe the entire load with a rag.

I use a very high oil content lube, and if I leave the bullets to cool the lube fully, the lube doesn't adhere and flakes off.  Thus, inserting the bullets while the lube is still warm.  I know that won't work for breech seating, but I suspect you would use more sticky lube.