I have a strop. It has leather and wool felt. My question is, do I need another felt strop for CrO or diamond?

My understanding is that I use the felt then the leather for stroping. For touching up a strop with some sort of paste is good.

Do you need seperate strops, or can you clean off the paste, or should I use the back side of my existing felt strop?

What kind should I buy if I should for the paste?