Does gun violence correlate with homicide more than all-weapon violence?

On my recent post I made a hypothesis and wanted to further investigate homicide rates related to gun violence. I hypothesized that gun violence is more responsible for homicide rates than violence in general. The basis of my hypothesis was comparing neighbourhoods, primarily in St. Louis and Winnipeg, which is a Canadian city. When we looked at the violence other than homicides, the Winnipeg's worst neighborhoods were a little bit worse than St. Louis's worst neighborhoods, being that they had higher sexual violence, higher robbery and higher major assault rates, but the neighborhoods in St. Louis had higher homicide rates. Here's a quote from that post: "of the neighborhoods in Winnipeg with an aggravated assault rate between 3000.0 and 3300.0, the average homicide rate is 81.8. In St. Louis, the average homicide rate in neighborhoods with such aggravated assault rates is 212.6, 2.5 times higher." And my thought here was well, in St. Louis, there's a lot o...