According to ISAF, you do. We already held a Worlds with our Wave Class. We were threatened that everybody who participated in or helped with the event would be punished by losing their eligibility to sail in major ISAF-sanctioned events like Olympics, Pan American Games and ISAF World Championships.

We were also told that the host country would never be allowed to become a National Governing Body for sailing and would never be able to put a boat in the Olympics.

ISAF claims to control sailing in all its forms throughout the world, racing and non-racing, and claims possession of the words "World" and "International."

I guess the answer to your question is that, No, you do not need ISAF approval to hold a world championship if you are not an ISAF Class and if nobody in that class cares whether they get punished by ISAF or not. But ISAF can make things very difficult for you by threatening the host country and threatening race officials and by scaring away people who might want to participate but are afraid of the sanctions because they DO want to be eligible for major ISAF events.

That is the only way ISAF can "control."