Removing a hydrofoils stabilizer and riding the stock wing ie riding stabless increases the control requirements of the rider as the wing is unstable since nothing counters the wings center of pressure as it moves around the center of gravity. Furthermore there will be limits to the wings ability to function.
The design of flying wings is well researched. For home builders who wish to pursue the development of flying wing specific hydrofoils - here are some simple design suggestions.
1. The stabilizer and tail are replaced by a reflex which is a rectangular area on the trailing edge of the wing angled upward acting as the stabilizer
2. The wing should have some dyhedral which will help counter yaw-pitch-roll inherent in flying wings.
3. The wing should have two fences on each wing, and on both sides of the wing. These fences forward point should start behind the center of gravity
4. Small winglits on the wing tip should be installed to increase the Center of pressure area of the wing.
5. The wing shape could be designed symmetrical ie cambered both top and bottom. This would reduce center of pressure movement, increase the stability, but reduce lift.
There are plenty of pictures of flying wings. A primer for home builders can be found here.
The aerodynamics of flying wings part one and two
Light and frost has begun a flying wing project and will post for community use as the wings are developed and tested.