Is it possible even if the skin under the eyes is thin?

I am looking into surgery because of the bulging under my eyes, but I am a little worried because my skin is on the thinner side.

I was wondering if there was a possibility that the skin might look thinner or fine wrinkles might become more prominent after fat redistribution.

I would like to know if you check skin elasticity and thickness as well, rather than just looking at fat protrusion. Are there any specific points that absolutely need to be addressed during the consultation?