you will want to track down the duplicate files and delete all but one copy (you may want to make a back-up first). then open the other assemblies that use the part and re-direct them to the remaining file. (depending on the export algorithm and setting used in solidedge, you may need to reposition/remate the part as well) and then save.
Any chance you have PDM? If you do I would create a folder structure in the PDM that not only allows you to have a secure place to store these, but can keep revision track of them just in case something happens to a file and you have to revert backwards.
If you don't, create a secure location on a portion of your network. Work on these files one track folder at a time. Then and only then when you get a folder looking the way you want it, copy it to this network location.
I agree with Jeremy in that you are going to want to delete duplicates once you find that they are no longer needed.
Sounds like a very tedious task. Take it slow my friend.