I've been soaking in a laundry sink or transport tub for 20 years. Seems to work.
Good DUST CAPS are WATER TIGHT.....easily. This is simply a non-issue. If yours is not, get a decent one.
When I first started diving, I followed the lead of my instructor and just tossed the whole reg set in the rinse tank to let it "soak" for 10 minutes or so, making sure the so-called "dust cap" was in place. As I recall, my instructor said that it's called a "dust cap" like your watch is called "water resistant" rather than "waterPROOF"--out of an abundance of caution. Nevertheless, those were rented regs I was using at the time, and when I bought my own, I became much more careful about it--keeping the first stage higher than the second stage, etc. Recently--probably as a result of SB-induced paranoia--I acquired a 40 cf tank that I use to pressurize my regs during several hours of soaking.