If your goal is to use composting instead of the black tank and convert the black tank into a grey tank, then you can leave the black and grey valves both open. If the valves are situated on the same drain pipe with a down stream valve. Otherwise you may have to do some plumbing and/or pumping if the two tanks are not on the same main drain pipe.
However, a Blue Boy or similar container is not that big and if you are only taking grey then you can use a collapsible container. If you can lift a 5 gallon jug (50lbs) you can drain the grey through the garden hose cap on the main drain cap. Or if you do not want to lift the jug, you can use a pump to pump the water up to the back of your vehicle and drive it to the dump.