For what it's worth:
I don't have a reference, except a description in Jadoo, a book by John Keel. I have no particular reason to think that this book is accurate in any particular - it seems, if I'm recalling it correctly (I read the book a long time ago) to be a sort of hybrid of Baron Munchausen and Aleister Crowley - in other words, largely invented. However: even books of tall tales usually have an underlying layer of accurate observation, upon which the fabrications are built. This bit is more plausible than most.
Keel describes cobra catchers in Egypt carrying straight razors as part of their field kit. In the rare case of an unfortunate accident, they will promptly lop off a finger that gets bitten by the cobra.
This is actually a reasonable proxy for your zombie bite. Cobras have a documented tendency to hang on and chew rather than delivering the lightning strike characteristic of vipers with their more effective hypodermic fangs. From the Fascinating Earth article on the King Cobra:
Scientists estimate that the king cobra, with large poison glands containing highly potent neurotoxic venom, can deliver 120 times the amount of venom needed to kill an adult human. Moreover, to make sure it delivers an ample amount, the king cobra hangs on when it bites, chewing away at the wound so that the venom penetrates.
Again, I don't know whether Keel's account is truthful; but it certainly is plausible.
If cobra catchers really do use emergency amputation to save themselves from the highly toxic venom of cobras, then it would follow that emergency amputation would be a reasonable means of preventing your postulated zombification.