The magic item description does not say.
The description for the necklace of fireballs states:
You can use an action to detach a bead and throw it up to 60 feet away.
This does not tell us what happens if we detach a bead and don't throw the bead. Thus, it is entirely up to the DM running your game what happens when a bead is detached without the intent of immediately being thrown.
I would rule that once a bead is detached, it's a ticking time bomb and will explode at the end of your turn if you do not throw it. Why? I can throw the bead straight up into the air, and it still detonates when it reaches 60 feet above my head. This tells me that it is not an impact explosive, but rather a timed explosive.
Alternatively, you could rule that the magic of the necklace just knows when it is being used to explode things. The necklace description also says (emphasis mine):
You can hurl multiple beads, or even the whole necklace, as one action.
I can hurl the whole necklace, beads still attached, and it still knows to explode - it knows that I used my action to throw it. Just ask your DM before trying to execute this plan, because it seems to me that there are legitimate reasons for either interpretation.
But we can sidestep the issue entirely.
You get a free object interaction every turn. One thing you are permitted to do with this is:
hand an item to another character
So if your group were huddling close together, and the character holding the necklace happened to roll the highest initiative, they would be able to use their action to throw a bead, and then hand the necklace off to the next person. Just be careful not to throw it at them.
But you should ask your DM if they're okay with this too. Remember, initiative is a game mechanic - and the characters are not aware of game mechanics. If your table is averse to blatant metagaming, this strategy may fall under that umbrella, so you should discuss this before trying it.