Apologies for the delay in replying. (I did try to reply yesterday but the connection I was using, in a café in Cologne, suddenly dropped out).
You should be able to uninstall Outlook 2003 and then install, say Outlook 2007, without losing any data, as your .pst files should be preserved. That's confirmed here:
https://forums.techguy.org/threads/upgrading-outlook-2003-to-outlook-2007.646569/
That thread contains a link to the 'official' way to back up .pst files. An alternative is simply to ensure that Windows Explorer is configured to display hidden files and then to run a search for *.pst (which finds all files of that type). Copy those files to a USB drive, or similar. If your old .pst files aren't automatically found by the new version of Outlook, simply replace the new (empty) ones with the old ones from the USB stick. (I've used that method to transfer Outlook Expess's .dbx files from one computer to another on several occasions).