I think you can still use your sx injector, you just have to load a different payload onto it. Doesn't the sx dongle let you pick on boot whether you want to go to SX or load another payload? You could just place it on the root of your sd card for the dongle to detect it and you just select that to launch atmosphere.
Just follow the guide to setup atmosphere, but when it comes to loading the payload put it on the sd card like I mentioned, then use the sx dongle and load external payload then select the fusee-primary.bin (unless it auto selects it, I don't have that dongle though so I can't see for myself).
There's also this website that turns the fusee-primary payload into a boot.dat. I have no idea if it works well, or at all, but here's the
link (I'd assume it works, but hopefully someone can add their opinion on it)
You'd have to do that every time the primary payload gets updated though, thankfully every update of atmosphere tells you if the primary payload was updated or not (so you don't need to redo the payload every atmosphere update, just when the fusee-primary.bin is updated)
Also I stupidly thought you had the modchip, but if it's just the dongle then you don't need SpacecraftNX so I've edited that comment so it doesn't cause any confusion, sorry about that.