As far as I know, there is no built-in shortcut for hiding the clock.
But you can create one using NirCmd:
NirCmd is a small command-line utility that allows you to do some useful tasks without displaying any user interface. By running NirCmd with simple command-line option, you can write and delete values and keys in the Registry, write values into INI file, dial to your internet account or connect to a VPN network, restart windows or shut down the computer, create shortcut to a file, change the created/modified date of a file, change your display settings, turn off your monitor, open the door of your CD-ROM drive, and more...
Download and install NirCmd.
Create a shortcut on the desktop (or anywhere else) that executes the following command:
nircmd.exe win child class "Shell_TrayWnd" hide class "TrayClockWClass"
Save the shortcut and edit it (right click → Properties) to assign a keyboard shortcut to it.