Pack and go is the tool you want for this.
Pack and go shouldn't effect the original. When you pack and go, do you change the file names in any particular way? If not you run the risk of 'confusing' SW with files it has stored on your RAM regardless of whether you've closed them. Add a prefix or a suffix or a find/replace on the files you wish to copy within the pack and go dialog.
You can also deselect all the parts you don't want to copy, say if you have a standard component folder, you can use the filter to deselect all files in a certain location. The options are endless, explore them. http://www.youtube.com/watch?v=-2_CH9HSbgo
As Bjorn said, Pack and Go shouldn't affect the original file. One thing that bit me a few times was when I would do a Pack and Go of an assembly, then start editing the assembly that was open. Could that be what happened to you? If you make sure to close the assembly you did the Pack and Go on, and then open the new one before making any changes, you should be fine.