Thanks to the tip by Jon Davis, I found the following workaround for the somewhat-annoying error:
Cannot load Windows PowerShell snap-in [..] because of the following error: No Windows PowerShell Snap-ins are available for version 1.
when opening a new x64 Powershell with the PowerShell Community Extensions.
The workaround? Simply run:
C:\Windows\Microsoft.NET\Framework64\v2.0.50727\installutil.exe "C:\Program Files (x86)\PowerShell Community Extensions\Pscx.dll"
from an elevated command prompt.
Hopefully, this may be of some use to others...