They treated them the Same as they do now for the most part: they stop the bleeding with pressure, keep it bandaged, treat pain as needed with narcotics. (Cocaine was a topical anesthetic. If your care giver was real fancy he may have stitched up his patient. Both opiates and cocaine were over the counter then.)
If the person providing care was well read then he might have been aware of germ theory (which was about 20 years old then) then they might have used a form of antiseptic on the wound - phenols, carboxylic acids, etc. "Listerine" was an antiseptic solution for wounds that went on the market in 1881. The same tan liquid stuff that is sold as a mouthwash.
Internal cocaine increases blood pressure, and opiates drops it, but they would be more worried about his heart rate. They would know if the patient was faint when he got up - so they would just have him lie down.
They couldn't measure blood pressure for another few years.