Now I know lots of folk are going to find this hard to accept, but it's the truth, and I think the more experienced here will back me up.
Firing shots over the heads, or even at, wild game doesn't alarm them a bit.
If you hit something close to them, and that makes a noise, that will spook them, but the shot itself has no apparent affect.
I base this on many years of hunting.
The MNR even recommends firing shots to scare away a cow moose if you shoot the calf and she stays. (doesn't work in my experience)
Shooting at running deer. If you miss, the deer won't even change course, unless it sees you, or the bullet strikes something close enough to alarm it. Even then, it's more likely to stop, and look about than fly off in a new direction. Unless of course it sees you move.
No I've no experience with Grizzly/Brown bear encounters, but I honestly wonder how many folks have tried to scare away a bear with a shot, and paid the ultimate price for doing so.
They make bear bangers, because shots don't work, you want the disturbance to be right beside the animal. They tell you to shoot them close to the animal. People in polar bear country will tell you that even then they don't always work.
IMO, making yourself known to the animal, making sure it knows you walk on two legs, not four, letting it get your scent, is the surest way short of shooting the animal dead, to getting a swift departure on the animals part.
The exception being polar bears, and probably some grizzlies/brown bears, that see everything as food.
This may not work on a moose, or black bears for that matter, depending on the circumstances, but It does seem to give them pause. They are well aware that they have few equals in the bush, but they have limited or no experience with humans, and as such may (repeat may) be more cautious if they figure you out.
Yeah, I've been there for a bluff charge by a moose when I had no cow tag and I shot the calf. We did fire shots, she just stood there staring us down. When I separated from my hunting buddy, she charged him, and only stopped when I ran back to him.
It's not an experience I'm in a hurry to repeat. If it happens again, I will stare straight at her, waive my arms, jump around and yell like an idiot, and do it quickly, so she has no chance to feel me out. If she starts to leave , follow her up at a run yelling. That works far better than gun shots. Or has in calves I've shot since.
BTW, be wary while you are gutting, I had one cow come back. I was done gutting, stood up, and there she was 20 ft from me. I never heard her coming. She could have stomped me dead, and I doubt I'd have known she was there 'till she hit me.