Richard,
I would recommend doing this on a Wire EDM, as it will be a faster and more repeatable process. You can use 0.004" wire to achieve the smaller than 0.003" radius. You can also look at using 0.002" or 0.003" wire and achieve a smaller inside corner radii, but the level of difficulty jumps up significantly. Using 0.004" will not be an issue on modern Wire EDM machines if properly maintained. I do not know what your Surface Finish requirement is for the part, but I would recommend performing a 2 or 3 Pass Process to make sure you achieve your geometry radii size target.
The issue I see performing this via Sinker EDM is the need to use multiple electrodes to ensure the radii requirement, as the electrode will break down on a sharp corner detail. Sinker EDM will also require that a fine finish is produced on the part to meet the geometry radii requirements, making the cycle time longer. The electrodes will also need to be redressed and re-machined for each part to ensure consistent quality, so it is the longer cycle time and electrode manufacturing requirements that make Sinker EDM less attractive.
I hope this is helpful!
-Brian