You would have to do a thorough study of the extent to which men would commit suicide if they did not have a gun, and if they would (and many probably would), what other method would they use.
That’s exactly what the Siegel study referenced did. Go back and read more closely. They looked at gun suicides vs total suicides and calculated the replacement factor from their multivariate analysis. It really is quite good work.
Now, how valid it would be at the “no guns” boundary condition is certainly questionable, because their relationships were built from a data pool with no data down at the zero boundary. But the replacement factors you’re talking about were taken into account in their study.