The shortest ones are Conquest Mongol bows, and Hungarians like already mentioned. The horns don't really need to touch in the grip, you can make a larger celik to match.
Generally, 35cm solid final thickness is the minimum, +40cm is better. E.g. 4 or 5mm thickness to the end. You can let the last 5cm towards the knee taper out, but having an even strip that you can taper down later is always better and more controlled.
Turks "can" have the horn run to half the kasan, but that depends on your sense for security.