I have done a few caps and quite a lot of other thin leather work.
It is possible to get thin leather down to around 0.5mm. Almost all leather used in clothing will be thicker than this.
If you want thinner than this (down to 0.3mm), you will have to use snake/sea snake skin or Shagreen (ray skin) - all of which are perfect to work with.
There is at least one very good supplier on e**y (UK).
With thin skin you can cut just past the bends and use the traditional velvet for the internal surfaces.