As policy, if something can be done via the registry, I would steer clear of third party apps offering to do the same thing. Freeware apps could be a nice way for a company to promote itself and there are trustworthy ones out there but sometimes, Freeware could also be a way of injecting your PC with a nice piece of spyware for purposes of identity theft and fraud. I've even found fake Open Source projects on SourceForge that were packing spyware.
I've uploaded my registry patches for you. It's easier then try to get super user's formatting to play nice.
Remove Previous Versions (.reg files)
http://www.mediafire.com/download/zy2bnld84k6yc97/Previous_Versions_Remove_and_Restore_Context_Menu.zip
I don't know about Cut, Copy, Delete, Rename as I use them and have never had reason to remove them but if I find a way, I'll update my answer. I'm running Win7 x64 sp1 pro. I would make sure the info in the restore .reg file is consistent with the entries in your own Windows registry before merging the delete .reg file (you never know if these things change across version of Windows). Just use the ctrl - F and F3 to search for the code within curly brackets {}.
EDIT:
Have searched around through the forums, it seems that the consensus is that Cut, Copy, Delete, Rename are not things that have registry values that can be modded (or they are unknown). I did come across a tutorial on how to mod shell32.dll.mui files to remove built in shell entries using Resource Hacker: http://www.sevenforums.com/customization/170036-remove-create-shortcut-file-folder-context-menu.html . That unfortunately requires the installation of 3rd party software for Resource Editing. There is Resource Hacker by Angus J. It's not open source but he's been maintaining the project for 16 years and the latest build has 0 hits on Virustotal.