Remove wrinkles from silk sport coat, advice, please

I just received a sport coat I ordered from The Territory Ahead. It is a silk "tweed". It came folded and bundled into a plastic mailing envelope. Needless to say, it has wrinkles.

The fabric care instructions are "Dry Clean Only". I don't wish to pay to have a never-worn garment cleaned for the side effect of removing wrinkles.

Who has trustworthy advice for wrinkle removal?

Use a press cloth (lint-free tea towel if you have nothing else) over garment as you press. Use a sleeve board or rolled-up towel as a pressing-ham to press areas so you don't press in more wrinkles. Take your time. Don't get it too wet.

Whatever you do, don't engage in the 'hanging in steamy bathroom' caper.