Reapers are space ships. It doesn't matter if their designed after the shape of a water-dwelling creature. I could make a car the shape of a fish but it wouldn't swim. And it's highly unlikely their weaponry could penetrate to the depths that submarines maintain. In atmosphere, they can't even kill a person when striking withing 5 meters.
Even if the Reapers managed to knock out the missile subs, there have got to be smaller scale tactical devices that would still be able to destroy a Reaper.
Reapers aren't sapce ships onnly. They are clearly cabable of walking around on firm ground as well. Nothing leads me to believe the only terrain they can't handle would be water, considering:
1)Again they are designed after an aquatic race.
2) A Reaper was sent to deal with Leviathans, who are underwater.
3)The cataclyst managed to defeat an aquatic race at least once before. I doubt he would create minnions that couldn't handle harvesting another one. If they couldn't funktion underwater, what would they do if there was an advanced aquatic race? Say: "Noooo! We can't do it. We'll have to blow of the cycles. Sorry guys lets search another Galaxy to torment." This clearly doesn't happen, as they attack this cycle although the hanar are auactic.
While we never saw if Reapers swim, it seems very unlikely they can't
Also the bolded part is just Shepards shamefully obvious plot-armor.