Reliable mortality statistics following early 19th century wound care are a little hard to find. However, following the battle of Waterloo, military surgeons treated about 100,000 injured men, with an in-hospital mortality rate of 9%. The majority of these injuries were inflicted by musketball and artillery and cutting/stabbing weapons. Note that's 91% survival among patients who lived long enough to make it to the surgeons, not all soldiers shot, stabbed, or bombarded on the battlefield.

Circling back to your question, the answer would have to depend on the degree of wound contamination and the severity of the wound compared to a typical Waterloo injury. Assuming a non-contaminated soft tissue wound, however, survival rates could be expected to be better than a musketball injury. Infected wounds would be much more dangerous. There was little any physician or surgeon at the time could do once erysipelas, tetanus, bacteremia, or gangrene set in, other than amputate the extremity and hope for the best. Some infections could be survived however-- a local contained infection, that is, an abscess, could often be drained surgically without turning into a bloodstream infection.