Two things.
1. Disney already uses wrist bands for other things. If they felt they were getting ripped off by having people swap them, they would change the system. They love money.
2. A centralized measuring (can be at parks, hotels, many locations to ease traffic), would also come with a waiver. Parents would sign off on "I acknowledge my child's height is appropriate for all rides 40 inches and below" or something like that. Then if a parent is able to magically get the wristband swapped and something happens to the child, Disney is protected.
Win-win-win
Borderline taller kids win
Disney has legal protection if parents abuse system
Cast members at rides have responsibility / stress taken away