Home Depot, and probably Lowe's as well, carries 'project wood' in sizes/lengths/widths perfect for making strop blocks/boards. Wood available is usually poplar, red oak and perhaps a third option that escapes me at the moment. These are well-finished & smooth, and take very little prep work (if any) to adapt for this use. Thicknesses range from 1/4" thru maybe 1" or so, and there might even be some in square dimensions, such as 1-1/2" x 1-1/2" or so. Lengths from 24" thru 48" (maybe 60"), and widths from around 1-1/2" up to maybe 6" or so. I've used the red oak in 1/2" thickness x 2-1/2" wide, cut to desired length. The strop block seen in the pic below was made from just such a piece:
I've also seen some 'paddle' shaped boards in soft wood for hobby/craft projects at Hobby Lobby. Some of them are pretty big, but look like they'd be easily adapted for these uses.
A simple paint stir stick can be found at any Home center or hardware store. They're FREE as well; can't beat that. Not real wide or thick (maybe 1-1/2" x 1/4" thickness), but they'll do. I've noticed Home Depot has them in a somewhat longer length (maybe 24") for larger paint buckets.
David