I'm pretty sure you only get to "electrocute" yourself once. Especially in 1743.
I wonder- his lack of grounding may just be what saved his life. If the mentioned chain connected to the outsides of both jars were grounded then there might have been a short across his heart.
But in common use it just means to receive an injurious electric shock, nowadays.
The chain was probably the cell ground? Unless the Leyden jar had a different ground wire, which seems improbable. Likely he got it straight across the chest.
I suspect a dictionary might accept it as an 'informal' alternative to the main 'death by' definition.
Laziness subsided, my Collins (complete, 2016) - which is a rather accepting dictionary of new-fangled words or usages - has only two definitions, both involving death. (1. to kill as a result of electric shock; 2. (US) to execute in an electric chair).
chortle (chuckle/snort) podcast (ipod/broadcast) newscast (news/broadcast) sportscaster (sports/broadcaster) motel (motor/hotel) email (electronic/mail) blog (web/log) bit (binary/digit) chunnel (channel/tunnel)
I still prefer the specificity of death for electrocuted. Keith Relf was electrocuted, if you can still talk about it, you received an electric shock.
Edit: spelling. Make Englyish great again!
A lack of grounding would preclude the conduction of electricity. As this is HV, a small spark gap would not have helped remarkably.
For nonlethal electrical mishap, just "shock" is fine, and "electric shock" to disambiguate when there may be confusion with emotional shock from excessive surprise or physiological shock from a traumatic injury.