While I recognize that Hudsons remarks arent much more than bravado. Its not unusual for soldiers to have their own nicknames for some of the equipment they use. I think Gearbox was expanding on the idea, by bringing the 2 together.
The "Sharp sticks" in Hudsons context was meant as more of a melee weapon, I make this assumption based on its pairing with knives. Its probably some sort of cattle prod in a literal sense. Atleast that is what I always assumed.
Gearbox seems to have designated it as a type of ammunition. Which makes more sense than it just being a gun, gun type etc. SHARP (Gun) Sticks (Ammunition, that sticks in things).
Should be fun for setting up traps.