I use pre-cuts, held in a tin box, like a "Sucrets" tin. I pour in lube prior to going shooting, let them saturate then pour off the excess, barely, but gently squeezing the stacks of pre-cut patches to run off the excess. When on it's side, it doesn't quite drip- but only just barely. The patches are WET!, not just damp. When seated flush with the starter, there is a very small ring of water queezed from the patch, all the way around the patched ball - this almost gets sucked up by the patch above the ball, but since it's saturated, not all of it disappears. This is for target shooting.
I heat oils a minor amount, especially mink oil, to allow them to penetrate the cloth completely, then gently squeeze out the excess with my fingers - slightly. When loaded flush with the muzzle, there is a ring of lube or grease (mink oil is a grease when cool) around circumference of the ball. When using mink oil, this ring will be white in colour. Loading is as easy or easier than with water based lubes in all of the guns.