It is possible to get compressor units and a fairly stable humidity.
One guy does it (Cigar Climatology) he's a bit full of himself, though. My take from it is basically get an active humidifier, and some beads or KL. You will definitely need a temperature and humidity controller - there will be overshoot both cooling and humidity wise.
Alternatively, without all the hassle just get some Tupperware and store that in the cooler with Bovedas or beads in the Tupperware (sealed) with cigars. Which is a lot simpler and easier.
Depends on how much overshoot and fluctuations you can live with. You should be able to keep it in the high 50's - 70%. It will just overshoot when the cooling comes on. The humidifier will easily get it there. Seeing as it's compressor I'd probably go for the bigger units, perhaps an Accumonitor or the larger Hydra.