The horn relay handles all of the "big" current. They use them so that they can use daintier horn buttons and wiring.
If you do wire straight through, go and buy a starter button for a tractor and wire it to that.
I tested my horn by running a line from the batt terminal on the regulator to the positive side of the horn (the ground was wired straight to the manifold clamp) and it worked very well.
