I would try to fold up a towel and put behind her for him to stand on and hold her (which you should be doing anyway) so that she can not pull away from her.
I'm not sure about frozen, just because I've never dealt with it before. I would think that you could take them both to the vet an have it...um, "transferred"...right away without having to freeze it? Of course, that would only give them the equivalent of one tie...hmmm....
I hope you get some more input as I am interested to hear opinions on this as well.
