Save a few bucks and get a case! MGM has good prices on basic cases. Without a case, your uke is competing with the outside world for the moisture in the humidifier.
Now, since you've spent your money on a case, make your own humidifier. Buy a pak of Cello sponges from Target or Walmart. Cut a small piece of sponge, dampen it, wring it out, and put in into a zip lock bag that you have poked several holes in.
I use a piece about 1 inch by 3 inches for my guitars when needed. I would use a piece about half that size for a uke