Clean fresh water is the last rinse your reg gets when it is serviced. It is then dried, lubed, and assembled. It is unnecessary to get it serviced. It does need to be dried though. Remove the HP hose so you don't force water into your SPG. If it looks dry, your SPG should be fine. If not, remove the SPG from the hose and reconnect just the hose to the 1st stage. Best at this point to also remove all LP hoses. With or without the SPG hose, put it on a tank and run some air thru it to dry the HP & LP sides of the reg. With the 1st stage dry, reconnect the HP hose or SPG, reconnect all LP hoses, and connect your inflator hose to an inflator. Pressurize it again and run some air thru each of your 2nd stages and the inflator to blow out and dry the LP hoses any water remaining in the LP side of the first stage. Some may say that the inadvertent flooding may wash away the lube and they are not totally wrong. But the lube is fairly water proof and is little effected by what you did so it should be fine. I would not waste too much time getting it done. Even FW may leave deposits if left to evaporate. It should not be enough to be harmful in any way, but no reason to push it.
If that sounds like more than you want to do, take it to your LDS and see what they will charge to dry it out. I would think a fair charge would be around $20. More if they insist on disassembling and relubing the O-rings.