"Swords" are usually shaved done on the sides and out of the back blades with a plane or spoke shave, once taped they can be no less than an inch and a quater in diameter and may be fitted with a thrusting tip, which is required to have and inch of progressive give and may not double over.
Thusting tips are usually contructed from close cell foam with a leather collar around the area that the rattan and the thrusting tip are joined to prevent doubling over.
Axes are considered a mass weapon and thus cannot weigh more that 4 pounds, the head can be constructed out of several materials, the most common being close cell foam (like a camp mat) and must have progressive give over the whole head.
Maces often have a foam head with rattan splints attached to the outside, this is then taped over and is usaually attached to a handle(haft) that is relatively short and is also considered a mass weapon
It is a good idea to shape the handle of your weapon so that you can tell if you are hitting with the "blade" or the "flat" of your weapon.