To be honest, you'll have the same issue with underarmour as you will with spandex. They're both super figure hugging.
What are you using to make the skirt? I'd be inclined to use the same material.
Tshirting would also work fine, especially if you can find a cotton one with a good thickness.
Can I ask, why would you take out a bit in the back? To make it more fitted? If so, you should just reshape the side seams.