This sounds like the older SKS system for attaching the fenders. The pieces grabbing the fenders were out of plastic and the grabbed fender edges were also plastic. The fit was relatively tight. I doubt you would get a match to the Wald fenders and an effective grip. You might consider the current SKS system and rivet brackets, which bolt to stays, to the Wald fenders. I suspect you might be able to buy replacement brackets for SKS. A bike shop might have such brackets left from broken up SKS-es.
Yeah the planet bike one's work this way: the bits "pinch" the fenders and it's a tight fit.