My non JW father died because he signed the "no blood"paperwork before he had heart surgery. All he knew about blood transfusions is what he learned when he studied with the Witnesses decades ago. He only signed those papers because he was a bit squeamish about blood and his doctor assured him there was no way blood would even be an issue. Two years later they came out with the new light about blood fractions which may have saved him had it come sooner. I'm certain he'd have seen the contradiction in allowing fractions that were taken from a blood doner's arm yet prohibiting the use of whole blood. He'd have realized that these men should not be in the habit if dispensing medical advice.
Be sure you have a counter argument for Deut 12:16 where it talks about not eating blood. They view transfusing blood as being the same as eating it. They compare it to alcohol. If a doctor tells you to abstain from alcohol but you put it in your veins, it's the same as if you drank it. To me that example doesn't compare apples to apples since the motive behind the prohibitive against blood isn't a medical one but because god said not to eat it because he views blood as sacred. Putting alcohol in your veins will have the same effect on the body as drinking it does. Eating blood and transfusing it would have two very different results. This scripture was talking about animal blood and besides,transfusing blood hadn't even been thought of. If blood is sacred and life is in the blood,why not use it to save a life rather than pour it out on the ground? Also there are any number of medicines that would harm you if you ingested them but would cure you if you took them intraveinously(chemo,certain dosages of antibiotics etc) to use the alcohol analogy seems logical at first but to me isn't enough.
P.S. I don't know why you have to even talk to these guys. I think I'd find out what your leagal rights as a father would be if a blood emergency arose.