I don't disagree that a non-gun killing can be similarly or more deadly compared to a gun killing. The point I take issue with is that they can be interchanged such that a person who would commit a gun killing would instead commit a non-gun killing with similar effectiveness.
I also agree when comparing US deaths to deaths in, say, England, it's inappropriate to suggest the sole difference is access to firearms. It is certainly a variable that can't be ignored, but it's one of many variables.
I'm cynical to the point of assuming any legislation, whether reactionary, related to firearms, or something else entirely, is poorly thought out and ineffective. My point, which may have been poorly stated throughout this thread, is that we could do better than we are doing. I don't have good suggestions for how to get there, unfortunately, and with politics and culture the way they are, doing better may be impossible.