I have been substituting apple sauce for oil for years now. The cakes turn out moist and you can't taste the apple. The only downside is that the cakes may be a tiny bit sweeter so I try to use unsweetened apple sauce. If you try this, I would start with just one of the cakes and see for yourself.
If you have olive oil, at least you would be substituting one oil for another....
Here's a thread on that:
http://forum.cakecentral.com/cake-decorating-ftopict-90341-.html
If the cakes you're making are from scratch, I think that using melted butter wouldn't have the desired results; cake mixes are much more forgiving of additions and substitutions.
JMHO
I googled this and every site said sub with olive oil or another liquid oil. Butter has too much milk fat and will change your recipe.
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