Thanks everyone, for the tips!
I have some sewing machine oil called Zoom Spout-"highest quality turbine all purpose lubricating oil" that I bought at a sewing machine shop in Woodland (this for Sewnoma since you're so close you might know of the place). I'll use this if people think it's ok stuff, otherwise brand recommendations are welcome.
I do like the baby wipe idea just for convenience (if it's safe for baby butts it's safe for sewing machines?) although since I have the oil already the wipes seem unnecessary.
OK, off to un-tape Cecilia before it gets any hotter around here. Is goo-gone safe for removing tape residue on the outside of the machine?