It is helpful to distinguish between natural hazards and the disasters that can result from them. Natural hazards become disasters when the built environment and the social, economic and cultural systems haven't taken them sufficiently into account. These natural hazards existed before there was was climate change, have been exacerbated by them, and will exist after climate change is solved. This doesn't fully address your question, but Susan Keiffer, a geologist, has suggested we call disasters caused any human activity "stealth disasters" since they are not sudden events but are the result of cumulative actions over time. What is good about this characterization is that solutions to stealth hazards are based on modifying human behavior (such as reducing greenhouse gas emissions) that are different from mitigation efforts to address natural hazards. It also helps tie in other sustainability concerns such as drawing down aquifers which is causing subsidence issues, reducing pollution which is harming ecosystems, etc.
I think that it is difficult, if not even impossible to relate an individual natural hazard to climate change. What often is done in the media, e.g. saying: "Hurricane Katrina was caused by climate change" is scientifically unsound. What we can do is to analyse and come to the conclusion that we an increase in average global temperature the incidents or intensity of hurricanes have statistically increased. So we relating disasters and climate change statistically, but not saying that there is a causal relationship of a particular hazard with CC.
The other issue is that a disaster is not a natural event, but an event of society. Strictly speaking it is wrong to say 'natural disaster'. If anything is 'natural' then it is the hazard and Disaster Risk Reduction is the effort to achieve that a hazard does not become a disaster. So, Climate Change and disasters are even less connected, as a disaster is an event that happens when societies are not well prepared to deal with hazards.
This year's hurricanes and cyclones were more powerful and destructive than in previous years. That suggests the sea is warmer than usual. To cool the sea one needs to cool the air. In order to cool the air, one needs to stop burning fossil fuels in cars and factories. When your car is running do you notice that the engine gets very hot? That is wasted heat that heats the air basically. A proper efficient engine should not heat the air!