My 7 yo wore hers last year. I was initially concerned that she would have trouble keeping track of it, but she did a pretty good job. We took the removable outer edge off and it fit her wrist pretty well. Throughout the day, I'd periodically look down to make sure she still had it and she always did. The only time she lost it was in the lazy river at I think Blizzard Beach. She was rough housing a bit with her uncle in the water, and we realized right away when she had lost it. It had floated a bit upstream, but it took less than 5 mins to find it. The next time we go, I will probably just not have her wear it at the water parks as there's really no need for a kid to wear one there. For her, a lanyard wouldn't have worked as well as I can't ever get her to keep those around her neck and I'm not a huge fan of her wearing things around her neck on certain rides where they could potentially get caught on something. It all depends on the kid though.We didn't want to put her entitlements on a keycard as not all of her shorts have pockets and sometimes the adults spilt up with the kids so it would have been a pain trying to remember to pass off the keycard to whatever adult she was with so she could use her FPs.
The other option that I had considered was putting the puck on a keychain and attaching that to her belt loop. Unless your kid is pretty tall though or you get a retractable keychain, you might have to take the keychain off when they need to scan it for FPs as the scanners are a bit higher than a child's waist level. Also bear in mind that not all shorts have belt loops.
Overall, try not to worry too much. If you're staying on site, I know you can go to the front desk at your hotel and get a plain grey replacement magic band if you lose yours and they can swap everything over/ deactivate the old band. I'm not sure how that works if you're in the parks when it happens or if you're staying off site though.