A number of people, from Steve Leavitt to Michael Moore, have compared
gun ownership and violence rates between other countries (e.g. Canada,
Switzerland) and th eUS and concluded that US gun violence is far
worse per capita, even controlling for the presence of firearms.

I want to know what the rates are in the US when recalculated based on
the relative distribution of handguns (and, if possible, short-stock
rifles such as Uzis and Tec-9s), or, put another way, what happens to
the rates of gun violence when rifles and shotguns are excluded?

This is really two figures: what percentage of gun violence in the US
is really handgun violence, and what percentage of homes wiht guns in
them have handguns?