Yup. Moving both characters (and apparently stash files) from Main to Custom requires GD Stash - as it is the only available tool that provides the option to properly flag them as “mods” so that the game properly reads them as such.
Edit: Well, I guess that’s not entirely true…
Odies tool will work as well. It is a command-line tool tho so if you are comfortable with such you might consider using it instead if you would rather use something lighter than GD Stash.
Tho… I am unsure if it can do anything with transfer stash files or not.