Just my .02 here as a journeyman cabinet maker.
If the part you want to use as a humidor is at the bottom of the cabinet it looks like it opens from both sides. I would secure one side, seal the corners with a thin bead of Silicone II or III, then a single thin coat of Zinnser Bullseye Shellac. Both will dry with zero odor after a few days and insure no humidity issues with the cabinet.
The Spanish Cedar, Cedrela Odoraa for the humidor needs no gluing. A couple brad nails here and there to keep it in line are sufficient as it will move around a bit with humidity.
Make sure to find a thin latex or silicone rubber seal for the door. Most repurposed cabinets like this do well with some kind of lock to keep the access door pulled shut for a tight finish.
I'm jealous, this is a great score.
Oh, be careful with the lights, make sure they are switchable to 110 volts, most European appliances use 220. If you replace them I recommend L.E.D.
Hope this helps.