Humidor Humidifiers

This should be a simple question, but it has me (and google, apparently) stumped.

If I stick a typical humidifier to the lid or back of my smallish humidor, how do I refill it?  I can’t pour water into it without turning the whole works upside down.  That means I have to take the cigars out, turn the box over, pour in the distilled water, take the whole thing to the sink and drain off the water that didn’t soak in, then bring it back and refill it.  This is dumb.

Currently, I am simply not attaching the humidifier – simply standing it on edge at the back of the box, and taking it out to refill as required.

There must be a better way – they all come with adhesives, right?