With all due respect, Cockrum v State was more about keeping weapons out of the hands of certain classes of undesirables such as slaves and thugs for the benefit of well-to-do white folks than it was about public safety.
By contrast, of the public safety risks identified in Heller, emphasis is on keeping any and all firearms out of the hands of convicted felons, the mentally ill and sensitive places. No exception is made in Heller for the possession of weapons that are less dangerous than others, as in Cockrum. The focus is on the safety of the general public, not the danger to individuals from onerous weapons in personal altercations.
The latter is the province of statutes dealing with prohibited weaponry. Insofar as those are found to be in conflict with the Second Amendment's no infringement provision, neither is absolute, and the courts are bound to reach a conclusion.