Yours is similar to what I did for my chrome polishing compound, except I took a short cut or two. I glued the horsebutt strop to the bottom board and glued the sides only to the top board, so I didn't need to saw it apart. That probably resulted in my wasting more time fiddling with the fitment of the side strips. I figure a horsebutt strop charged with chromium oxide is much harder to keep clean and easier to contaminate than a diamond plate or natural stone, so making a covered container for it is higher priority than my other sharpening media.
I made one improvement by gluing a strip of wood across the bottom a couple inches from the front end of the box, so I could clamp it in my shoulder vise to keep it from slipping around.
I used 0.3 micron dry Cr2O3 powder that I mixed with mineral oil. To apply it to the strop, I loaded the mixture into a syringe (Monoject 412), making a big mess in the process, squirted a little onto the strop, and spread it around with the first edge I honed on it.