Your home or your shed .... where will the finished item be stored once you are done working it? That's probably a key consideration to make. Some people keep their in-home air conditioned with added moisture for better comfort .... a home that is very dry results in cracking of mucus membranes and discomfort of one's lips and nasal passages ...
My brother happens to need a humidifier, as such dry conditions causes him to have nosebleeds for no apparent reason whatsoever. I wouldn't consider his idea environment to be perfectly dry, but he doesn't keep it humid enough for molds and moss to grow indoors without watering the plants (not that he'ld keep mold around, but I wouldn't put him past a zen rock garden and a terrarrium).
In any case, it's probably best to dry the wood down to under 5% moisture content right before you stabilize it, as the wood fibers will naturally attempt to draw any kind of liquids into them quite deeply ... adding pressure to force the liquids even deeper would result in a superior stabilization. If you are wanting to use cactus juice or other stabilizers, kinda similar to wood hardener, then the plan to dehydrate the wood is a great idea.
If you are just drying out wood that you've recently cut down and milled .... stacking them level on stringers to allow for proper air flow and keeping the rain off the stack (keep it under a roof) for a few months is best, for large quantities. If you just have a few branches, perhaps a small log that you've obtained, with just enough to fill the smoker .... then I would suggest taking the door off and putting the wood on the smoker shelves and letting them air dry naturally. Once they're dry, then mill the rough boards down to pen blank (or other blank) sizes.
You could use heat to speed the process, but it isn't really necessary, and as long as the moisture content reaches equilibrium with your shop that should be good enough for everyday use.