What about carrying a mixture of 38's and 357's in the gun? E.g. Have 357 ready to go but if you have the time you could rotate the cylinder to 38? And for a dog you could use a light 38 load, right? So the hearing issue could be even less than using hot 38 rounds.
I was out in the desert years ago, and some pinhead cranked off 3 shots from a .357 4", I think it was a Ruger Security-Six. I wasn't any closer than about maybe 150 feet and it was pretty bad my truck was suddenly very quiet inside. I can't say I've ever personally heard any handgun round worse than a .357 as far as hearing damage potential, that crack is something else. But in a life and death situation, who cares about your ears?