I'm not sure the mute will stay muted after a shut down.... Which is why I suggested using external speakers that have their own volume control as an actual knob that can be clicked off, lol. The volume control on most laptops is software based... to save space and in the case of the 8886 to allow the use of a remote without a motorized volume knob, lol. So, I believe the software resets to the volume you had it at when you restart... but I don't think that includes mute. I will try right now, though. :-)
As I suspected, it doesn't keep that volume setting until you get back into windows... So that solution won't work unfortunately. :-( I'd say go with the others suggested, though. Best of luck!