Winter Soldier Wig

I bought this cheap wig for my Winter Soldier Costume (I don't have much money or many wig options). I think it's good enough for the job, but I need a way to flatten it. It has way too much volume for my costume.

I heard that I could use a water spray bottle to flatten it (with hot water?). I don't think I could get a better wig than this without looking online. I've never used a wig before in my life, and my natural hair is way to short for the job (a buzz cut). If anyone has some tips, please go ahead and tell, I need help with this wig.