Hunting Alligator With a Bowie Knife

In Shooting and Fishing in the Rivers, Prairies, and Backwoods of North America (1865), Benedict Henry Revoil mentions having met a man who required neither firearm nor ammunition to harvest alligator:

On the Texan coasts and about Lake Sabine there are vast salt marshes . . . where alligators abound, and where they grow to a size elsewhere unknown. Here you may see these enormous brutes stretched out in the sun and displaying their proportions as if they were perfectly at home.

One day I happened to be on the shore in a tavern, 
and near a landing-stage where a boat called for New 
Orleans, and there I met with a hunter named Allen, 
a man who lived on the Angolina River, and who 
came every year, from November to April, to employ 
his time in the catching of alligators. This Indian 
Nimrod had a companion named Jim, who was of 
the Bolaxis tribe. Jim was a better sportsman than 
his master, for he never needed anything but a lasso 
and a bowie-knife to get the better of an alligator. 
If he saw an alligator, he crawled cautiously towards 
him and lassoed him, and soon put an end to him 
with his bowie-knife.