I'm currently dealing with this problem. I throw a party for a large number of relatives. This year a great niece, at the age of nine developed a tree nut allergy. It has become a challenge to even avoid foods with hickory flavoring added to sauces, rubs and hot dogs; and foods that been processed in plants that also process tree nuts. I'm not taking any chances and using only fruit woods, or maple wood to smoke. I can do that with my charcoal and pellet cookers, (which reminds me I need to send an email to Bradley to see if their apple, and maple are a pure as possible); since I'm sure they process the apple and maple in the same facility and equipment they use for pecan and hickory.
The reason I'm being so cautious with this is that I have a reaction when I use the cherry bisquettes, I develop an itch and a headache, and if I breath in any smoke I have trouble breathing.
While I was (and still am) researching this; do a google "does smoke from nut trees affect those with nut allergies"; that will bring up a lot of sites. It seems like the overall feeling is "Maybe! Don't use nut woods to smoke with, to be on the safe side".