What to clean bare wood with after sanding?

I'm getting to the point that I'm starting to sand putty spots and get the "fuzz" knocked off the outer skins before I stain.
What do you guys use to get all the dust off with? My first TTT, I used a tack cloth but found it left threads in the wood. Paper towels were even worse.
I don't have an air compressor (
) so that's not an option. Maybe a sponge soaked in thinner????
Jeff
What do you guys use to get all the dust off with? My first TTT, I used a tack cloth but found it left threads in the wood. Paper towels were even worse.
I don't have an air compressor (

Jeff