I often use moisturisers or cuticle oils, etc, but have a touch-screen reader (Kobo Glo, previously Kobo Touch). It's infrared, not capacitative, so all you have to do is break the IR beam with a very light touch. When my fingers are really oily, I just page-turn with a tap from my knuckle. Works fine, and the screen has a "rough" papery texture so it doesn't show the smears.
Otherwise, I guess you're looking at a Nook or a T1/T2, out of the major vendors. The bottom-located buttons on those are, as noted above, inconvenient to use, and there have been reports that the T2 buttons are also sharp/uncomfortable to press. Of the bebuttoned readers I've tried, the Kindle buttons are the nicest to use, but yes that would involve conversion. Bulk conversion with Calibre is a piece of cake, though.