I might be wrong, but I don't believe you can have both versions installed on the same computer at the same time. I believe the executable programs have the same name and would cause a conflict with the operating system. I suppose you are aware that Lightroom 6 will not be able to read the catalog you have been using with Lightroom Classic. Right?
Why on earth would you want to go back to Lightroom 6 if you also want to upgrade your OS to Catalina? While Lightroom 6 may run on Catalina, it's just a matter of time before you will get into trouble. If you ever need to reinstall something or reregister, you will be screwed.