First, natural disasters include earthquakes, volcanoes, and other phenomena not related to climate change. Second, the 370,000/year average from the 1950s/60s includes two years with some of the highest death tolls. If you look at the full range of dates, there are a lot of peaks and troughs
Quotes from above: The trend still holds when the measurement is narrowed to weather-related disasters, which decreased similarly as a share of global GDP even as the dollar cost of disasters increased.
Also, from the website: What we see is that in the early-to-mid 20th century, the annual death toll from disasters was high, often reaching over one million per year. In recent decades we have seen a substantial decline in deaths. In most years fewer than 20,000 die (and in the most recent decade, this has often been less than 10,000). Even in peak years with high-impact events, the death toll has not exceeded 500,000 since the mid-1960s.
This decline is even more impressive when we consider the rate of population growth over this period. When we correct for population – showing this data in terms of death rates (measured per 100,000 people) – we see an even greater decline over the past century.
As for claims that there are more hurricanes, I don’t think there is high confidence in that from the IPCC: ‘Average tropical cyclone maximum wind speed is likely to increase, although increases may not occur in all ocean basins. It is likely that the global frequency of tropical cyclones will either decrease or remain essentially unchanged’
This is taken from the latest IPCC report