According to a representative from the NYC Poison Control Center, this shouldn't be a concern. While gel sanitizers often contain more than 60% alcohol, it evaporates very quickly. (Part of the alcohol's purpose, after all, is to help the stuff dry quickly so you aren't all gooey afterwards.) Even if you were to rub a bit on your hands and immediately reach into baby's mouth, any amount of alcohol transferred would be insubstantial. That being said, you should keep bottles of instant hand sanitizer out of reach at all times — baby could suck or chew on the bottle, and the contents can be harmful if more than a teaspoonful is ingested.
If you'd rather baby didn't teethe on your hands, there are plenty of teething toys to keep him occupied, from classic rubber rings to stylish Chewbead jewelry for you. A frozen spoon can do the trick too.