can I put baby oil or cooking oil on my sculpture?

[XxxxXXMuffinzXxxxXX]

I made a sculpture of crayola air dry clay and I painted it. Now it's dry and I want to give it that glossy proffessional look I want to put some oil on it but I'm afraid it might peel the paint or. Make it come off, can u tell me. If I can or not put baby or cooking oil on it.thxs if not wat can I put on it

 

[humpty dumpty]

I wouldn't do that. Can you spray it with polyurethane?