Misunderstanding. The Asymmetrical sail is attached to the boat using 3 connections.
The Head, the Tack and the Clew
The Head, like for all sails, is attached to the Mast. The mast is attached to your boats keel and held in place by the rigging. The mast exerts downward pressure on the boat driving it forward.
The Tack is attached to the bow of the boat. To provide added trim control the sail's tack is often attached to a line. This line is run through a block attached to the bow. You pull down on the tack and the force is transmitted to the bow of the boat not your rigging.
The Clew is attached to the stern of the boat with a sheet to a block.
View attachment 191535
The only attachment point to your "rigging" is at the head where all of your other sails attach.
Properly sized and rigged to your boat in light to moderate winds strengths you should have no problem flying an asymmetrical sail on your boat.
A Sprit is often used to extend the asymmetrical sail out beyond the boat, but is not a requirement. A Sprit will add complexity to your boat and systems.