Typically one of the reasons for toning a print is for archival considerations. In the case of selenium toning the silver is converted to silver selenide. This is more stable.
If you are wanting to not tone the print. Then I would say that double bath fixing would be important followed by a thorough wash.
Will this be archival? I don't know (I probably will not be alive to determine) but it will be the best that can be accomplished without toning.
I have prints that were made over twenty years ago without being toned and they look as good today as when I made them.