I assume we're talking about the common microfiber cloths? They probably won't get into the grooves well, but are great for cleaning camera lenses and such. If they get dirty, just wash 'em.
You'd be surprised what "doesn't" get into the grooves.
But with any cloth, at what point will you condemn its use and reach for another? Once, 50 times, or ?
I will agree with other posters, that a simple vintage Discwasher or Parastat Brush would be superior to any towel-cloth.
For simple dusting, acquire a small 1oz Plastic Dispenser Bottle, from perhaps a Beauty Supply Shop, fill it with Distilled Water.
With the Discwasher Brush, you apply a few drops of Water to its leading edge and spread with the edge of the bottle is all.
As you use it on the Record, and the platter rotates, either motor driven, or spun by hand, you "rock" the brush, and the fibers help pick up dusts-caca. And if bad, yeah, you will see what it picked up. and when you then look at the record, you see it will now look in "playable shape". And help your Stylus-Cartridge from riding through all that "Doody".
The Discwasher and Parastat type Brushes can be periodically cleaned.
I'm not going to lie, I came up through the ranks, and I used such above for many years, and this is my findings.
Some of these records I have are 30-40-45 or more years old, yeah, that hI bought them myself brand new that long back. And that so many years later, they play superbly.
Te Discwasher evidently didn't seem to cause any significant degradation, or damage.
I did graduate over the last 20 years with different products-methods, I still have 2 vintage Discwashers, a couple types of Parsastats, some Watts Jobs, etc etc. And they'll go with me to the grave.
Beware about buying Discwashers today, there are I understand some newer clones which are said to be pretty crappy, and they are not the real deal.
I believe I still have my original Discwasher in brown woodgrain cardbord box from 40 years back. Still works like it did when I bought it! LOL