There really is no need for a treble hook and no need to tie separate versions with and without a stinger.
While I don't use stinger hooks on any flies, I do use single “trailer hooks” on spinnerbaits which work just fine.
If I were so inclined for streamers, I would do the same thing: find a long shanked, ring eyed streamer hook with an eye opening large enough so that you could thread the point and barb (or not) of your fly hook through it.
Get some vinyl tubing or surgical tubing in a size that will fit over the big eye on your stinger hook. Slide a short piece of tubing over the point of your stinger hook and slide it up and over the eye. You can do this in advance and stash the hooks in a small box or Ziploc bag.
When you are ready to add it to a streamer, just push the point of your fly hook through the tubing and the big eye of the stinger hook and slide the stinger hook around to the bend of your fly hook. BTW – you will have a much better success rate if the stinger hook point rides UP.
Removing the stinger when not needed is just as easy if you don't have a barb but a little trickier if you do however, you can just cut off the tubing completely and replace it later.
If you feel compelled to do it with treble hooks, just cut off any unwanted hook points with wire cutters and dab a little head cement on the cut marks to retard rusting. I use to do it that way with in-line spinners when I was a kid to reduce snagging and it works just fine.
Also, if you can't find a stinger hook with a big enough eye (which I doubt will be an issue), adding a small split ring will work too.