TeraCopy is also in the Alt+Drag menu so it can use used without registering it as default copy handler in OC or in Windows (has to be installed though), but the goal with Taskmaster is to eliminate the need for Explorer dialogs and also the need for TeraCopy.
I have not used TeraCopy much myself so know what its limitations are, but Explorer's system has a lot of limitations, some of which I have mentioned on that linked page.