Raritan markets their "C.P. Cleans Potties" only as a toilet bowl cleaner, but it's also the best sump and drain cleaner on the planet. It's a bio-enzymatic cleaner than not only destroys odor on contact, but the enzymes in it "eat" the hair, soap scum, galley grease etc that build up in drains and clog sump pumps.
Somehow you need to block the drains so C.P. and water can stand in 'em at least overnight...the enzymes in it need time to work. Put 2-3 oz of C.P down the drain, then fill the drain up to the sink with clean water. It won't harm anything even if you leave it in the drain for month, it just won't do anything more after the first 24 hours. Open up the drain an run clean water through it.
If you have shower sumps this would also be a good time to put a few ounces of C.P down the shower drains when it can stand at least overnight. In fact, a weekly dose on most boats will keep sumps clean and sump pumps free from clogs...it's the only maintenance job on a boat that requires -0- manual labor.
If there are P-traps in your drains, there shouldn't be...they serve a purpose on land but just cause problems on boats. Your drains need to be as straight a route to the thru-hull and/or gray water tank as possible.
Discharging gray water direcly overboard is legal in all US waters except for a very few closed inland lakes that you're unlikely to visit. As others have suggested, you should have the ability to drain gray water directly overboard, 'cuz maintaining a black water tank is a walk in the park compared to maintaining a gray water tank! Why do it if you don't have to? A y-valve, a length hose and new above-waterline thru-hull is all you'd need.