I've been cleaning records with soap and water in the sink for nearly 50 years and never had a problem with a damaged label, though I usually try to be careful with getting the label too wet, and I don't have especially valuable records (though maybe they are now). More recently I use Liquinox instead of dish soap for the surfactant (it rinses better), a soft boar-bristle shaving brush to get the surfactant into the grooves without damage, and a final spray with an alcohol solution + wipe with a microfiber cloth to expedite drying. I have a label cover I made from round outlet covers (perfect size) and a bolt, but I hardly ever use it. Vacuum machines remove the dampness and deep-seated dirt better (I still hear some pops after cleaning my way), and there are attachments for your canister vac (or even full 3d-printed machines) available for cheap on the auction site. As I understand it, the main advantage of tergitol over liquinox is that the ionization is opposite, and so the tergitol-cleaned record is less likely to attract dust after cleaning. I live in a humid climate, so this has not been especially noticeable.
There are long and surprisingly sober and informative) discussions of cleaning on some of the other forums that are more dedicated to vintage gear.