For all the reasons Jason explained^ so well, the bar/stick compounds are kind of a pain to apply to a leather strop, and likely won't work so well because of that. There are ways to heat & melt the stick compound, to make them easier to apply; but the waxy binder is something that I never liked on a leather/wood strop in the first place, and I feel it just gets in the way of the stropping process, when done by hand. The compound loses a lot of it's polishing aggressiveness in all that waxy mess, on a strop.
I've liked using a dry, powdered green compound purchased at a lapidary/rock-hobbyist shop, sold as a tumbling medium for polishing stones. I bought it in a 1-lb. jar for about $18, when I purchased it maybe ~3-5 years ago. It can be easily mixed with mineral oil or some other suspension of your choosing. With mineral oil, it mixes pretty easily and can then be 'painted' onto a strop of whatever material you're using. The coverage is dense and very even and a little bit of the dry compound goes a very, very long way. I use maybe an 1/8th of a teaspoon of the powder, dropped into a disposable container like an empty margarine tub or yogurt cup. Add mineral oil and mix to a paint consistency, and use a small paintbrush to apply it. Give it a few hours, or up to a day or so, to dry. Wipe away the excess with a dry paper towel after it's dried.
On very hard leather or wood, like mdf, basswood, maple, etc., this method works very, very well, and it's my favorite method by which to use green compound.
