The Prince of Wales has never said any such thing. If a magazine article said he did, it was lying.
Besides anything else, he would not have the power to do that. A King of the United Kingdom can abdicate - in which case somebody else would become King (William, if Charles abdicated). He cannot dissolve the monarchy. Parliament has that power - the King does not.
I'm still hunting for the article, but I did read that. It was an interview with him; IIRC it was an organic gardening magazine. He did say that he would disolve the monarchy because it had outlived its purpose. The main focus of the article was on HRH's green views of things and his farming practices. The monarchy quote may have been a throw away, but it was in the piece. I'll send the link once I find it; like I said, it was 10-15 years ago.