I have the #1 pick in my world this year. I don't see a player worthy of the #1 pick (this may be one of the worst drafts I've seen in recent years), and I'm considering punting to next season to get a comp pick. If I'm successful in drafting a dude who doesn't want to sign, what pick do I get in next year's draft?

If you have the #1 pick this year, you will get the #2 pick next year.

If you go to the Draft Order page and click on the help (?), you will get a popup. In there it states:

A Type "D" pick is the result of a franchise not being able to sign a non-supplemental pick from the first 3 rounds of the previous amateur draft. In order to receive Type "D" compensation, you must offer the draft pick his initial demands, he must refuse to sign the contract, and the contract must never be withdrawn at any time during the current season. If you are unable to sign your first, second, or third round draft pick you will be awarded a compensation pick in next season's amateur draft. The compensation pick will be at the same position as last season plus one except for unsigned third rounders in which a supplemental pick is added at the end of the third round.

For example, if you couldn't sign the 25th pick last season you will have a compensation pick next season and you will have the 26th pick (assuming there were no other Type D insertions prior to that pick).