I taught a class on suicide detection and prevention many moons ago. I recall that the statistics bore out your observations.
Women want to leave a pretty corpse. Men don't GAF.
I think I remember mafia guys don’t like to take it in the face if they can help it, so they don’t have to have a closed casket and their mommas can see them again.
Generally, that is true. I've known of many suicides in recovery programs over the past 35 years. Most ladies went with an overdose. One lady I knew closely did use a .38 to the temple.
The guys opted about 50/50 between a firearm and a high-speed crash. One guy hanged himself (no red scarf; just standard rope).
I prefer the Buddy Hackett plan - live to be 150, and get shot by a jealous husband.