Hi, my husband is preparing for RP so I found those on Amazon for him to try https://www.amazon.com/dp/B0DGT53JYL and he is very pleased with comfort. I ordered one size larger so they do not press on anything but still will hold in place pads and catheter etc. They are made of very soft cotton and elastic is also comfortable. He usually wears low rise briefs so I was trying to find something more practical but still nice looking. They have opening on the "fly" area so catheter can pass there and connect to a bag.

Regarding ice- it should never be right next to your skin. Same applies to icing any other part of your body. There should always be thin fabric between your skin and ice and pad should not be big obstacle for cooling effect to happen.