Can you recommend any that don't have iodine?
I rarely ever use cough drops, and I'm not allergic to iodine, so I don't know any specific non-iodine brands. Just go to the store and look at the ingredients on the label. Iodine will be listed if it's present.
Also, is that one reason you don't see many people carrying iodine towelettes around?
Oh, I don't know. You don't see many people carrying pitchforks around either, but that's not because they're allergic to them.

I suppose the real reason is that most people don't have much use for iodine towelettes in the first place.