strosfann,
The short answer is that you are on the right track, for casual paper shooting and small game hunting you do not need AO.
The long answer is that if you wish to shoot the smallest possible groups on paper then you need the AO and maximum magnigication so that you can define your aim-point better. All things being equal the difference in group size between a scope with AO and one without it will be about 1/4" at 50 yards. Past 50 yards there are a lot of other variables that enter into 22 lr rimfire shooting that generally have more effect than parallax.
Without knowing what sort of small game you are speaking of it is a difficult to state definetively that it will not be a problem, but I run a Leupold 3x9 without AO on my Cooper sporter and certainly have no issues with shooting gophers out to 125 yards or so. Parallax is not enough of an issue to cause a miss at the short ranges and the parallax is less of a factor further out.
Another avenue is this - buy a scope marketed as a shotgun scope, they are generally set to be parallax free at 75 or so yards.
drover
