Whether or not a younger kid can go is going to be entirely up to the CMs on your specific sailing and what you're willing to put up with. It's the Bahamas. It's almost certainly going to be HOT. It's a *boring* run for many adults, let alone a kid. And you do the loop TWICE. Yawn.
I left my son with his dad, sleeping in the room, the first time. I watched a kid's mom con a CM into letting him run. Later, I passed kid and mom, and both were utterly miserable. Kid was dragging, being like Russell in Up..."I don'wannnnn'tooooooo". Mom just wanted to run her event. It did NOT look like fun.
If there is another adult along, I'd leave the 7 year old with the adult. Or I'd make this one of those "I insist" moments. You'll be gone 30-45ish minutes.
And...everyone....remember that any one person's experience with what time you meet, what time you dock, what time you disembark as a group, whether or not there's room for joining in without pre-registering (that has NOT been possible the two times I've done it since they got more strict), what time the run starts...those are all highly variable and canNOT be expected.
On my second (?) CC 5K I saw a woman highly angered because she had arranged nursery time for *an hour*. And that time was up by the time we merely got off the ship. She thought the timeframe was an absolute, when it's merely a timeframe, a possibility. I have never once gotten off the ship earlier than 9 for the free island CC 5K. (January of this year I participated with the inaugural Castaway Challenge, a PAID 5K held with the marathon weekend events, and that one started before dawn...we docked around midnight to make sure we were there)
So just be aware that there is very little set in stone about it.