I know you can unplug and drain it from the button but it's a pain. I'm a big fan of the drain and fill but it is just too messy in this case IMHO.
I read that a turkey baster is a good idea but totally disagree. It didn't have a enough suction with the extension I used and when you squeeze the air would escape from the squeezing area (not sure what it's called) and spray small amounts of fluid everywhere. It was a complete fail.

But I found the solution but haven't tested it just yet. The solution is to buy or use a hand soap pump that has the straw attached to it so it squirts straight into a bottle of some sort.

Hope this saves someone the hassle.