I wouldn't chance it. Bully's are so allergic already. Allergies are like a pile of blocks. Each block is an allergy. You are building a tower on a carpet where it isn't to steady to start with. Each block of allergy that you add the more unsteady the tower becomes and with each block you get a symptom itchy eyes, teary eyes, itchy paws, hives. One day you put that next block of allergy on there and the whole tower falls over and you have a very sick dog. So even if your dog doesn't show a reaction to the salmon oil you already know it is an allergy block why put it in your tower when there are other options.
Why do you want to switch to something different?