I agree it would be nice if they wouldn't use the exact same connector for the water as for the argon, but I understand that from a cost prospective they only want to stock one type of part.

For my 2¢ if it was me, I would just cobble up some kind of connection to a garden hose or even just hold it up to a tap with your hand. Run water through it until it comes out clear. Then do something similar with air at low pressure to dry it out. If you have moisture in the hose, and try to weld aluminum, you will know in a big hurry if you didn't get it dry enough.