Here's how to remove the Run command from the Start menu:
1. Start the Registry Editor
2. Go to HKEY_CURRENT_USER \ Software \ Microsoft \ Windows \ CurrentVersion \ Policies \ Explorer
3. Double-click the entry NoRun and change the Value Data from 0 to 1
4. Exit RegEdit and restart Windows
To put the Run entry back on the Start menu, just change the value of the NoRun key to 0
You can also use my Tweaking Toolbox for Windows, one of it's functions is to remove the Run command from the Start menu.
For more information & free trial, check the Tweaking Toolbox for Windows pages. 
Remove Run command from Start Menu