Two sides felt and paste... Advice needed

Hello everyone,
I have a quick question for you...

I have a double strop, leather and felt (I think is felt) it's 3" wide and it's quite thick...
I'm planning to buy a few things for my birthday and among them is a two sided paddle strop, both sides leather. One side English Bridle the Other Black Latigo, and I'm thinking of getting some paste for the strop.
I was thinking of getting the TI paste in tube, which according to the description is mainly to maintain the edge of the blades. (10,000 grit)

My question is, would it be a good idea to put the paste to one side of the felt strop and leave the other side without any paste? would this be an issue? This would mean I'd end up with a two sided felt strop with different surfaces.
Or should I apply it to one of the two leather sides of the paddle strop?

I usually use the felt side of the strop after my shave to dry it thoroughly and a few passes to heat the blade before stropping it on the leather side.

Cheers.

E.