I advice a drainage system.... If you are misting for the longer duration times (2-3 minutes) then you will need it. I have a dragon strand drain pan. All my plants are elevated and nothing is on my floor. I run a mist king, humidifier at night, and a dripper. And I have quite a bit of water run off to where I have to wet vac the pan every other day.
Dragon strand now makes a universal drainage pan which will accommodate a 16x16 up to a 24x24 cage.
https://dragonstrand.com/alternative-cage-manufaturers/
You could use clay pots on the bottom which will help absorb moisture from the pan but I still think having a wet vac is important.