If your Steam version was bought before
April 2019 (or certain other cases
*) then you can run that account via a direct (non Steam) installation. You just need to make a copy of the non-Steam EDLaunch.exe file, rename it, run and log in using the Frontier Account details of the Steam account version. I have several accounts, including two Steam accounts (sales on Steam) all run from a normal non-Steam installation.
* When you look in your Steam library Elite Dangerous game if you can see "CD-Keys" then you should be OK to run without Steam. Some of the "HumbleBundle" bought ones are of this CD-Key version - surprised me and it ran from non-Steam installation.