Putting her under shouldn't be necessary. What my old vet used to do is to cut the nail really short and use a toenail buzzer - kinda like a Dremel tool - to smooth off and cauterize the blood vessel. I stopped having him do this for our dogs because it really upset them. And since we've moved, he isn't our vet anymore.

From what you say, probably muzzling Jo and having someone strong to hold her might be necessary to get this done. The vet may use a toenail buzzer or maybe just put styptic on the crack in the nail. Either way, I think it's important to make sure that it's not going to open up and bleed. You may want to call your vet and get his opinion - maybe you could put styptic on it yourself.

Hope this helps.