I frequently use a Dutch Schultz style of dry lube, usually 1 part Castor oil to 6 parts denatured alcohol. Patches are dipped and then left out so the alcohol all evaporates off and it just leaves a light coating of the castor oil, you can barely tell they're lubed. Same can be done with Ballistol and water.
Like Jon said, you'll have to swab between shots unless it's a really rainy or high moisture day where the fouling stays really soft.
My rifle's accuracy goes haywire after more than two shots without swabbing, at least with everything I've tried so far, and so I just swab every shot anyway.
The "dry" patches give me the best groups I've ever been able to get, except I've found that I can also get nice groups out of a very, very lightly lubed mink oil patch.