This should be an interesting discussion! OK, let me tell you, I am a bit of a purist. Nectar is only nectar when it is in the plant for me, and hasn’t passed through any other organism. If you extracted something from a hive, it is either honey, or unripe honey, not really nectar. Others may disagree, but bees do so much complex stuff to nectar after they harvest it (adding enzymes, drying it out etc), that I really can’t bring myself to call it nectar any more.
OK, now we have that out of the way, phew! Any honey that you take from the hive with a moisture content above 18.5% water is at risk of fermenting from yeasts which are naturally present in the honey and the hive. It is impossible to give a shelf life. It depends on how wet the honey is, how much yeast is there, and how warm your “shelf” is. That time could be weeks to months, and if you have jarred it, you can expect some lids to be under pressure from inside!
I really think that a honey refractometer is absolutely worth purchasing. That way you can be sure whether your honey is shelf-stable or needs refrigerating or even freezing. You can buy one for under $40 from Amazon - just bug the seller for the calibration block and oil if they forget to ship it (ignore the Robot Check message and just click on the blue text):
I actually have this one, thanks to @Bobby_Thanepohn, and I really like it. Easy to use, and seems accurate so far.
So the short answer to your question is, if you are not sure about how dry your honey is, you must refrigerate or freeze it. Yes, you can feed it back to the bees any time the temperature is above 50F outside. Honey from your own hive is just about the best thing you can feed your bees, even if it isn’t fully ripe.
Sorry if it seemed like a lecture, I am really pretty friendly! Please ask more if anything isn’t clear.
One more thought, if it does begin to ferment, don’t give it back to the bees, they won’t want it.