While the trawl net normally slows the player's movement once equipped, it's possible to bypass this by waiting to craft the trawl net until you're out at sea and first removing the boat's sail so that when crafted the trawl net goes right into the appropriate boat equipment slot. This will prevent the movement speed penalty from being applied.
Steps to Reproduce
Go out to sea, remove your sail, and craft a trawl net, which will immediately be equipped on the boat.
Go out to sea, remove your sail, and craft a trawl net, which will immediately be equipped on the boat.