Dwale: an anaesthetic from old England
“How to make a drink that men call dwale to make a man sleep whilst
men cut him: take three spoonfuls of the gall [bile] of a barrow swine
[boar] for a man, and for a woman of a gilt [sow], three spoonfuls of
hemlock juice, three spoonfuls of wild neep [bryony], three spoonfuls
of lettuce, three spoonfuls of pape [opium], three spoonfuls of
henbane, and three spoonfuls of eysyl [vinegar], and mix them all
together and boil them a little and put them in a glass vessel well
stopped and put thereof three spoonfuls into a potel of good wine and
mix it well together.
This stuff sounds wicked to me and also to the author. Either henbane or hemlock by itself would pack a punch (ask Socrates) and here they costar with booze. Apparently the original recipe also had mandrake root which does not grow in England. But if you are going to have someone sleep through getting cut, you need serious medicine.
There is a reference to dwale in Canterbury Tales too (see linked source) so it was a known thing. The only problem for the proposed use is that it would taste absolutely terrible because of the bile. I suspect dwale would need to be made fresh because the bile would not keep. Maybe the herbal ingredients are available in case someone needs to whip up a batch and your character just uses the henbane and hemlock parts for the poison.
I can imagine the healer (the author suggests this would not have been a barber-surgeon but some layperson) explaining to your character that she thought the bile was to keep the patient from drinking it too fast, because too much dwale was liable to kill. The bile made sure the patient choked it down little by little. In your fiction, the sleeping poisoned person is actually thought to be dead - he does not stir when slapped and his beard is pulled, and his heart is so slow (from the anticholinergic henbane) that he is not thought to have a pulse. People thought to be dead but not dead are the stuff of good fiction.