Safari from macOS Catalina not working on macOS Mojave
As jaume and ankii suggested in the comments below the question (and as per Apple Support), the way to do it is to reinstall macOS Mojave. I now have the correct version of Safari for Mojave and I don't seem to have gained any new problems doing this.

If anyone comes to this question looking to find a place to download a stand alone version of Safari for macOS, I don't think it exists - though I am happy to be corrected.