In the history someone cited that Unpaved p. 42 says directly that he "died of cancer." Then someone reversed the edit. We also know, as told on the next page, that Caroll Spinney spoke with Will Lee, apparently on the set, while Lee was "very ill" and four days before death. So, it was not an instant death -- unless he actually died of a heart attack while suffering from cancer, God forbid.
Also, that Wikipedia page also claims that show #871 is about Hooper receiving his GED, but, assuming our numbering is correct, it's only about him studying in the arbor.
(Edit) Okay, I searched Google News archives for obituaries, and most appear to say heart attack, while some say cancer. Thus, even as far back as 1983, people weren't sure. I realize also that if he was on the set filming, ill or not, just four days before his death, it probably wasn't cancer. (Not to mention the Thanksgiving Day Parade, too.) Good that the Muppet Wiki doesn't say.