The best feature in the Organizer for that purpose is the export function (not available on Macs before version 11).
Before exporting selected files, one good idea is to put the selected photos in an album where you can sort in whatever order you want. The export dialog lets you choose the destination folder, the format and size of your pictures depending on your purpose. You can even rename the files in the album order when they are exported.
If you are not sure which folder your images are located in, you can select a thumbnail in Organizer and the select the Information tab in PSE11 or right click and choose Show Properties in earlier versions.
The file path to your image will be shown and you can click to go directly to the folder location.
You could then upload directly from the folder using your originals, without affecting Elements provided you don‘t physically move anything.