CHE's and bulbs will both drain the humidity from the tank. Like other people have mentioned, it would probably be best for the snake and the humidity for it to be in a smaller enclosure.

I am trying to use a CHE for one of my enclosures now. I feel like I am constantly attempting to fix humidity and temperature problems. I really think it would be best to use 2 UTH's and thermostats rather than continually investing money and time to make a bulb/CHE work. That's just my experience, some people might tell you they have no problems with a CHE or bulb, it depends on the fluctuation of temperature and humidity where you live as well.