Living on the South Coast in Oil Field territory I've picked up a bunch of more or less 12" X 18" cotton towels. Many product and service companies have them marked with their logo and have a brass eyelet for attaching to coveralls for handy hand wiping.
Yes. I have a large set of bath linen dedicated to shaves. 36 white cloths (flannels for EU people) and 12 white hand towels. Bleached and blued weekly.
A suggestion would be to get a grommet set, and some good quality brass or aluminum grommets. Then you can take the nice cloths and put a ring in them. Add a "shower clip", and you have a set of easy to hang towels that aren't as harsh as the average golf towel. I've found most of those to be pretty nasty.
The brass grommets are still shiny, so I haven't considered stropping yet. Ahh. I am totally sports ambivalent. Don't watch 'em on TV, but I've enjoyed attending a few pro games over the years. It's an experience, but I haven't invested much time into being a Spectator. Now that I know these are golf towels... I sorted through them and moved all polyester blends to garage duty. The 100% cotton are either shave or kitchen duty. Since I shave at my kitchen sink it's the same thing. Why are bathroom vanities set lower than kitchen counters?
Kitchen counters are expected that you'll be doing work such as cutting, kneading, and other work that works best with your arms relatively level. Bathroom counters and sinks are lower because you're expected to be hand washing, face washing, hair washing, and things that will be best to be IN the sink itself when dripping. I suspect a very small amount is also that you're expected to have multiple heights in the bathroom, but only adults in the kitchen.