Dh has a severe peanut and nut allergy as well. We were at Disney last week and we were very impressed with how the restaurants handled his allergy. Dh usually just asks the waitress to let him know if he is ordering anything with nuts and if they are in doubt could they ask the chef. At several restaurants at Disney the waitress immediately got the chef and had him/her come to our table to let dh know what was safe and what was not.
Just let them know upfront and I think you will be good to go.