Change the keyboard shortcut for the HUD color picker ?

It sounds like you already know to select the color wheel in Preferences.

How would you like the wheel to work for you?  I am not sure if you could remove the right click aspect because you need that to actually select from the wheel, but I am sure you could reduce the Shift Alt shortcut to a single key, but I don't think you could do it from Edit Shortcuts.

What sort of keyboard do you use?  Is the tablet a stand alone thing with a screen like a Cintiq Companion, or is it more like an Intuos that works along with a computer and monitor?  If the former then I don't think the sort of keyboard you'd typically use with that would lend it self, but if you are using a full computer then you could use a gaming keybopard with programable G keys.  They let you apply multiple key combinations to a single G key, but I am sure you'd still need the right click.

Unfortunately Photoshop’s keyboard shortcutas are a bit of a mixture of customisable and non-customisable … I suspect this one falls into the latter category.