File>Save saves the modified version of the Sound, writing over the original in the Sound file. To save without overwriting the original, use File>Save as...
To save a Sound from the Sound Browser that you've modified, the best way is what you're already doing: Copy the rightmost Sound and paste into the Sound file window. Or click on the rightmost Sound and drag it into the Sound file window.
Also, when you edit a Sound from the Prototypes or from the Browser (by double-clicking to open a sound editor), Kyma makes a copy of the original and puts it into the "bread crumbs" window at the bottom of the screen. So when you use Save or Save as... from the File menu, it will overwrite or save a copy in that "bread crumbs" Sound file at the bottom of the screen. It will ask you if you'd like to save that Sound file more permanently to the disk.