Is it possible to hide Windows' Cut, Copy, Delete, Rename buttons on the context menu when I am working on an checked-out directory?

Solution 1:

No, this is hard as the folder isn't different in the registry and thus the menu entries can't be easily changed.

However, what about moving those actions to the main centext menu in the TortoiseSVN settings?

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There is a paste option at the bottom, I suppose it does the a rename action upon a cut item.