Believe it or not, electronic circuits aren't instantly ruined when they come into contact with water. There are two primary problems with getting electronics wet:
the water probably isn't pure distilled water alone, but has plenty of dissolved minerals (just take a look at the "dry residue" breakdown of a bottle of mineral water) that, once the water on your electronic circuit evaporates away, are left behind upsetting the conductivity/introducing paths for current to flow where there were formerly none
for circuits that feature a battery supplying power to the circuit at the time it gets wet, the now-wet circuit board forms a mini electrolysis experiment (because the water contains dissolved salts it's slightly conductive and when a current is supplied, parts of the circuit form anodes and other parts form cathodes) that causes some parts of the circuit to corrode, and other parts to suffer deposits of material. Left long enough a powered circuit in water will become ruined
It would be perfectly possible, even with complex electronics like a cellphone, to remove the circuit boards, wet them with distilled water, dry them out promptly and have them survive. The problem you'll have in just dunking your battery-less remote in the sink is that the water won't be distilled, and even if it were, it will rapidly become contaminated with tomato ketchup and no longer be pure water, but if there were enough water then the concentration of dissolved salts wouldn't be very high.
Most of the remotes I have come apart with a couple of screws; I'd open it up, remove the circuit board and then thoroughly wash the rest of the case. If that's not possible for you, remove the batteries and using a wet cloth hold the remote so the dirty part is facing down, clean it thoroughly keeping it held that way (gravity helps prevent water running inside it) then bang it on the desk a few times to knock the largest water droplets off and leave it to dry out. Remember that if you get water inside the case it will take longer to dry; leave it somewhere warm. It's not a train smash if it gets wet inside, as noted, so long as the water is relatively clean and free of dissolved salts. If it gets a lot of dirty water inside (because you do decide to wash it in the sink) then give it a good rinse with clean tap water then another rinse with distilled water (to wash the salty tap water off), and leave it to dry completely before putting the batteries back in.
It'll be fine; when my old XBOX clock capacitor leaked everywhere and wouldn't power on, I had no choice but to wash the circuit board in the sink with dish soap and a toothbrush , then rinse with tap water (distilled wasn't available) and used compressed air to blow the tap water off. It still works, 6 months on