So, if tackcloths are out and I don't want to make my own as you
describe, what about wiping off the wood with mineral spirits, thinner,
or alcohol? Do these raise the grain and require light resanding after
use as water does? I don't like the idea of having to sand again AFTER
wiping sawdust off with water -- it seems like an endless cycle --
water -- sand -- water -- sand...

I generally use mineral spirits if I will use varnish. With oil, nothing is
necessary.