I didn't find a way to set this, even via the right-click menu. Anyone could advise some? Thanks. :)
I didn't see an operator for this either, so you will have to write your own:
When run in the text editor, this will register the operator
One way to keep the operator registered so that you don't need to keep running things in the text editor every time you start blender is by including your operator text datablock in the default .blend and enabling Register in the header (see my answer here for more detailed instructions):
Note that your text datablock must have a
Aside from that, you might just want to make a complete addon.
I expanded gandalf3's example.
You can bind keys to call a menu or directly choose a specific brush.