Vegetable oils work well. I often forget to add this to my gig kit, so tend to use whatever I have in the cabinets at my house. Olive Oil, Corn Oil, etc - all of them have worked for me without a hitch.
Here is a link to "Lite" versions of clown white. The application is thinner than normal white; normally a substitute for warmer weather but it may be an option.
http://www.larocksmagic.com/makeup/makeup.htm
Ben Nye and Mehron links on the right both have Lite versions.
Also on that same page are some options for "soothing" make-up removers for sensitive skin.