Solution: Variable that contains current place from where the context menu has been called by clicking right-click on empty space i %V
.
So registry Command entry became:
"C:\Windows\System32\WindowsPowershell\v1.0\powershell.exe"
-File "D:\Run-CoolScript.ps1" "%V"
N.B. Of course D:\Run-CoolScript.ps1
has "to know" how to handle the input parameters!