Aug.126 at the bottom of the page has Trauma Surgery, but the threshold is "variable", so still up to you.
Table at Aug.127 has thresholds for implants, but those all take hours... A lot harder putting something in than cutting off a part.
Army medics in the field can do pretty quick amputations is the damage is too extensive and chance of infection far too high.
Silk's idea of "cut it off at the elbow, that makes sure the hand is unharmed and can be more carefully removed later" doesn't work?