Yea, I have a 100w lamp on my boa in a 4ft wooden enclosure and have no humidity problems. I also use cypress mulch which works well for holding in humidity. I have always had issues with glass aquariums and mesh tops... whether it had a lamp or not.

You might want to keep the tub, just in case.

If it is the ambient temps you are worried about, a lamp is your best bet. In that case you can place a damp towel over the mesh that the lamp is not resting on and spray the cage daily for humidity.