While the space bar doesn't currently lead to the muting controls, we do have some shortcuts available already...
Checkout some of the GoTo command shortcuts designed with accessibility in mind:
Be aware that the keyboard shortcuts work only when the GoTo is at the front of your screen.
If you are showing a PowerPoint presentation and the speaker is using the keyboard or mouse to advance the slides, any GoTo command you enter on the keyboard will go to PowerPoint, not GoToWebinar.
You have to click on the GoToWebinar window in order to use the GoTo commands.
And when you click on the GoTo Webinar application in order to use these GoTo keyboard shortcuts, then your keyboard and mouse are now NOT talking to PowerPoint.