craftgrrl | wrinkles in black vinyl

Hello crafty people! This is my first post to this community, and I really hope you can help me with this one!

I have gotten my hands on some black vinyl (at least I think it is vinyl - it looks a lot like faux leather, but I think it´s vinyl hence his rubber-y feel). I got is as a gift, which was simply awesome, but it has been folded up, well not folded, more crumbled into a ball. Yes, wrinkles all over... which was not so awesome at all.

I am planning to use it as backing for a "golden record" in a frame as a present for my Dad. The wrinkles HAVE to come out somehow or I can just ditch the whole project.

I tried ironing the back. Didn´t work. I tried ironing the front, with a damp towel over the vinyl and then ironing it carefully. No good results either.

Does anyone know if it would work if I would soak it in water and then air-dry it, laid out on a flat surface? If not, does anyone have any suggestions, I would really appreciate it!