Is foam or a wipe or baby shampoo best for cleaning sensitive eyelids?

A good option. Although there are several products on the market to clean eyelids, dilute baby shampoo on a wash cloth is one of the safest methods to use. First, have an eye doctor determine if you have blepharitis (inflammation and/or infection of the lids), then try gently rubbing the lids for about 1 minute with a wet washcloth that has baby shampoo on it. If the eyes remain or become more irritated, go back.
Warm water. Cotton tip soaked in warm water is probably best. Sometimes just a drop of baby shampoo in cup of water works with a cotton tip. There are over the counter stuff that utilizes foam or wipes for your eyelids as well, and they work okay too.