You probably won't find it online, you might check with
Special Dietary Requests there is an email there you can contact.
Generally, most beef items will use Mesquite or Hickory, while Pork & Chicken will avoid Mesquite and use more Hickory or Fruit woods (Cherry/Apple) the use of Walnut is more of a regional thing as the smoke is very strong. You also find a lot of blends too. I assume you know you are allergic to the smoked items with nut trees or being cautious?