substitute for oil when baking
You could use apple sauce, or prune substitute.
Probably the "safest" substituion in terms of matching the texture/moisture of what the origional chef had in mind would be to use extra-light tasting olive oil. It's right next to the other olive oils in the supermarket, but has less "flavor" than the usual EVOO.
There was a good article in the Boston Globe, I believe, about how lots of countries use olive oil in their baking (of cakes)...specifically places like Italy and Greece.
I usually substitute 1 for 1 apple sauce for oil in many recipes. Pumpkin also works well but since it is an apple cake stick with apple sauce but make sure it is 100% apple, that there is no added sugar. Keep in mind if you replace all the oil with apple sauce you will have a very different cake. I would start by replacing 1/2 the oil and see how it turns out. If it still feel/tastes too oily for you next time replace 3/4 of the oil.