In Dealing with a possibly gun shy dog I used 410 chamber mates through a 16 and ensured I did not shot directly over the dog. The sound was greatly reduced and the dog focused on the flushing pigeon and not the gun.
Actually silencing a SxS does not interest me
I have had two hunting dogs. A Weimaraner and presently a 1 1/2 year old Springer. Last summer, I broke my Springer by taking her out to the shooting club and held her behind the trap pad on a leash, during a tournament. The results were the same last summer as with the Weimaraner- 15 years ago......... First time-pretty scared. Especially with all the people walking past her. Second time still jumpy. Third and fourth times, wanted to romp and play more with the shooters than paying attention to the shooting, because everyone wanted to play with her. It never took long to get a dog of mine used to gun noise. Now it doesn't bother her at all to take her out to the club and tie her up while I shoot a couple rounds of trap. I worry more about the fleas and ticks in the area. It doesn't take long for them to get used to it. Good luck.