Ah, the beloved smoked mushrooms...we think they should be a separate food-group here...
Some folks haven't developed the taste for them, but we have, and find them to be very good as ingredients or as a garnish...for the die-hards, they make a great side dish.
Being you'll dry them, you'll want a low-temp smoke so they don't cook during smoking...80-120* should do fine...then dry at 135-150*. Lower temperature (both smoking and drying) reduces the loss of beneficial nutrients and may preserve the flavor, although it will increase drying time. Drying time is difficult to estimate due to equipment and environmental variables such as ventilation rate (amount of air flow through the
dehydrator/smoker) and average relative humidity during the drying process (higher R/H or lower air flow will increase drying time).
EDIT
Injecting smoke into a
dehydrator could be done with a Smoke Daddy cold smoke generator, although it would require quite a bit of smoke, and, the residue would build-up in the
dehydrator and difficult to remove if it got too heavy. The fan and heater element could possibly suffer as result, depending on the design.
END EDIT
Also, many, if not all, pre-manufactured vertical smokers (such as the MES 40) have a water pan. Use of water is beneficial for most hot-smoking, where as you will smoke and cook at the same time, though for your purpose with mushrooms should not be needed. Smoke needs some moisture on the surface you want it to adhere to, and the mushrooms will sweat some moisture during a lower temperature smoking process, so the smoke should stick just fine without the use of water in the pan. You may opt to add washed sand or pea gravel to the pan if a mass to avoid thermal warping of the pan is desired, but this generally is of more concern for hot-smoking, which generates much more thermal energy.
I did a bit of digging around on the net, as I've not yet dried mushrooms. I'll send you a PM with links. I did an advanced search here on SMF and no one has posted on smoked & dried mushrooms to date, but here's one on dried only...mostly just some discussion, but no "cut and dried" (no pun intended...lol!!!) on how to dry mushrooms:
http://www.smokingmeatforums.com/t/130635/dehydrated-shrooms
It sounds like your deli has some fine offerings. The addition of smoked goods is a great way to expand and share the smoke with others. I know this may seem overwhelming now, but when you get both feet firmly planted with smoked/dried mushrooms, you may also consider other smoked items, such as nuts/seeds, sea salts (for finishing dishes), spices/herbs, peppercorns...there's a whole world of smoked goods to be offered.
Be sure to check your local/state health regulations as you may be required to apply for a variance (per US Food Code...I haven't gotten that far in the 2013 code, but it was stated in the 2009 code) for any goods which you smoke that are offered to the public for retail. Packaging and labeling requirements are another issue, as I'm sure you know, but if you haven't previously offered on-site prepared goods, then you may not know. If sold from bulk containers and portioned at the time of sale you may only need to have storage/use/prep/nutrition/ingredient info printed and available upon request, but don't quote me on that. If sold in portion packages, that's another story. Definitely check into variance application requirements, though.
You probably already have access to this, but just in case you didn't know it was available online:
2013 Food Code
Let us know if we can be of further assistance.
Good luck on the new venture!!!
Eric
EDIT: BTW, Amazn Products and Smoke Daddy offer a good line of cold smoke generators which will make smoking far easier than using standard wood chips or chunks when cold/warm smoking. With cold smoke generators you can operate your smoke chamber temperature where ever you like.