You don't have to remove the shelter JW. I guess you meant the cowl, which does make it a little easier to get to the coolant drain plug.
This is how I did my coolant system flush. With the engine cool remove the right fairing pocket, reach down and remove the radiator cap. Then the 8mm coolant drain bolt above the oil filter.
When the coolant is all drained, I poured some distilled water into the filler neck to wash any crud out. I don't know if that done any good or not, I just wanted to do it. Then the put the 8mm bolt back in.
Now pour in the new coolant. The 1800 takes about 4 quarts. After three and a half quarts, start the engine and let it warm up. Then snap the throttle a few times to burp air out of the system, air will bubble up out of the filler neck. Burping all the air out is what takes most time.
Top off the radiator when all the air is out and replace the cap.
Heres a link to a photo gallery on how to do it. You dont have to pull the cowl to change it and I dont pull the overflow bottle. The overflow bottle you can fill and rinse and drain out. I use a handheld suction pump with a 12 inch hose to drain it out. If you want to get a better coolant go to a Honda car dealer and get the 5 year blue colored coolant. It goes 5 years or 50,000 miles and is premixed and is silicate free like the green coolant. I always use Honda recommended coolant. After you change it fill up the radiator and fill up the overflow bottle to the lower mark on the dipstick. Put on the radiator cap and fire up the bike letting it run for 3 minutes. During that time burp the radiator by blipping the throttle a few times. After 3 minutes shut down the bike and top off the radiator and overflow bottle. You should be good to go.