Here is a rare opportunity to get hard numbers of the lethality of arrow wounds. This book is A Report of Surgical Cases Treated in the Army of the United States from 1865 to 1871. In reports of 83 arrow wounds, 26 are fatal, or 31%. Excluding men who suffered multiple wounds, 21 out of 76 died, or 27%. Most of the fatalities occurred when “…the three great cavities, or the larger bones or joints were involved…”.
On page 86 there is an analytic review of gunshot wounds. At a high level, there is an 38% fatality rate.
I will look through later and try to exclude cases of multiple wounds, pistol wounds, suicides, accidents, etc. Since the soldiers are not using muskets by this period, the data is not entirely relevant. I will seek sources on musket lethality elsewhere as well.