I had several nevus type moles treated a few years ago - the ones that look like the rubber on the end of a pencil. Unfortunately it was my GP's first go at freezing moles off and she didn't do a great job. One dropped off and is now a flattened mark, but the others just scabbed up and are a bit smaller but still there. It's a pain when they catch on clothing but they aren't visible so I'm inclined to leave them now.
The freezing off wasn't painful and you just leave it to scab up under a plaster for a week or so. I would think it would be painless for skin tags.