The following pictures show you what happens when a service technician is servicing a regulator that this has happened to... it made a real mess all over my service bench....
Just be certain that you don't get any water into the gear's first stage. The internal parts are vulnerable to damage when they're exposed to water and moisture, so letting them get soaked will probably end up causing you to have to take your regulator to a professional to get fixed.
Prior to rinsing off your regulator, replace the dust cap, securely fastening it on. Of course, make sure the cap is dry first. Use compressed air that you could get from the cylinder in order to shoot excess moisture out of the dust cap prior to fastening it into place.
Rather than putting the first stage in fresh water to let it soak, just rinse it off completely in the sink. This will prevent water from seeping past its dust cap. Or you can instead completely submerge the regulator with the first stage attached to a pressurized cylinder. This will also prevent water from entering the unit.
Avoid pressing the purge button on the primary second stage or the octopus during the process of washing the regulator. This will let water into the first stage, which you don't want.
And if you do have hose protectors, be certain you thoroughly rinse beneath them throughout the cleaning process.
Move the low-pressure inflator connector in an effort to get rid of grit, salt, and sand to prevent corrosion and keep the unit performing at its best.
Once you're all done rinsing off the regulator, it's best to allow the unit to dry off completely by hanging it up in a safe place. Then simply store it away accordingly.
If in doubt, have it serviced.