Can I use oil in marinades for dehydrated mushrooms?
You can use oil in food you are dehydrating but you are correct that it will affect the shelf-life. The oil will become rancid before the dried mushrooms would have spoiled, but it will still be good for at least a few weeks and that can be extended to months, if you vacuum seal it.

If you want to avoid the oil, just skip it and use the spices in a bit of water (or diluted soy sauce, lemon juice, or vinegar). 

I haven't done dehydrated mushrooms, but I have made dehydrated spice mixes that contained some oil. They were fine and dried like anything else, but I didn't use a whole lot of oil in them.