whereas deaths from suicide by firearm alone account for a staggering amount of deaths (not all of which can be attributed to wanting to die unless firearm ownership somehow causes the desire to die to increase).
They don't increase the desire, but they do increase the success rate. Women attempt suicide more often, but men successfully commit suicide more often because women tend to use methods that won't result in scarring, like taking pills, while men use methods that are effective.
So, to treat this question fairly, you have to treat ease of playing as a separate issue from tonal quality. Also, even if you treat being intimate with the instrument as a necessity, you could still reasonably do a double blind test, assuming that the musician doesn't attempt to subvert the process. Give them two very nice violins, and don't tell them which on is the strad. If the physical appearance is too telling, then we might have to have a musician who is literally blind.