There’s pros and cons to both. I’ve never tried cervical dislocation (broomstick method) though.
If you cut deep enough, they do not freak out with throat cutting. The ones I’ve done just chilled and bled out peacefully, but you have to make sure you cut deep the first time. Some people have had them flip out of the cone and walk away.
Shooting is fine but the possibility of missing is real. They also don’t just drop dead, they often go into a seizure type flop and it can be very upsetting to watch if you’re not prepared, just FYI.