Yeah, like neigh on impossible!
What do you mean by "small game" - edible or varmints? I ask because a .22 Hornet, unless you load it down, is going to make a heck of a mess out of edible "small game" such as rabbits, squirrels and grouse - unless you can always shoot them in their heads. On the other hand, using various .357s and .44s, I've snipped the heads off more blue and ruffed grouse than I can remember. It legal here during the season, and there's no finer meal than blue grouse fried on a Coleman stove in a deer/elk hunting camp tent.
But if the "small game" you're talking about is only varmints, why do you care about how large of a "bullet" you're using?
Never-the-less, I repeat - you're not going to find a .22 Hornet revolver - which by the way, would be
LOUDER than you can believe.