A thread like this creates an opportunity to pass on some blunt and hard learned advice...
Don't ever be dissmissive or complacent about the risks of sanding and polishing by hand on rotating machinery - lathes, drills, .... We all do it but it is inherently dangerous.
I personally know a machine shop foreman with 50 years experience who had his hand torn off at the wrist in an accident when using emergy cloth on a metalworking lathe (admittedly more powerful than most woodworking lathes).
They took his hand to hospital in a crisp packet.
One day you will get distracted or have a lapse of concentration.
It's when, not if.
So in the spirit of learning from the other guy's misfortune, anytime you feel yourself start to get complacent about this task, remind yourself that people with more skill and more experience than you have lost fingers and worse.
They didn't set out to do it either and it was all their own fault (you are responsible for your own safety, if someone tries to make you work in a dangerous fashion, you walk !)
Use small pieces of cloth. Beware any piece of fibre long enough to wrap round or catch on the lathe or workpiece. Never wrap cloth around your hand or fingers for extra grip.
And do not ever wear gloves when your hands can come into direct contact with moving chucks, tooling, etc. Far better a cut than gloves being caught, pulled in and you lose fingers or a hand.