Removing the fuse won't stop the leak. The fluid from the washer tank is higher than the headlight washer jets. The fluid will just continue to dribble out until the issue is fixed.
The problem of dribbling headlight washers is caused by a spring loaded valve that lives behind the front lower grill. It holds the washer fluid back against gravity with a small spring. When the pump runs the pressure increases, moves the valve and the washers spray. When the pump is off, the valve closes.
When the spring or rubber valve wear. tear or jam, the valve no longer does its job and the car starts to cry.
Only fix to give washers that work is valve replacement.
If you don't want the washers to work anymore. Pull the electrical plug off of the motor or remove the fuse, and use a household clipit, or clamp of some sort to squash the rubber hose going to the washers. They have their own dedicated pump and lines so this won't affect the screen washers.
Problem with removing the fuse is that very few car fuses control only one circuit so you may find something else stops working too.