Add the watermelon to a blender and blend until liquefied. Strain the mixture through a fine mesh sieve and press out liquid with the back of a spoon.
Add the watermelon juice and sugar to a small saucepan over medium heat. Stir constantly until the sugar dissolves. When the mixture reaches a boil turn off the heat. Pour the juice into a 9×13 inch baking dish and whisk in the lime juice and rum if using. Freeze for 4 hours then use a fork to scrape the mixture into small bites. Freeze again and repeat the scraping process one or two more times within the next two hours.
When ready to serve, open the can of cold coconut milk and remove the liquid. Scoop the cream into the bowl of a mixer and beat on high speed with the whisk attachment until peaks form, about 2 minutes. If desired, sweeten with a bit of powdered sugar.
Serve in small jars (which you can prepare beforehand and keep in the freezer), top with a big scoop of coconut cream and a sprig of mint.