The ambient noise level in WDW parks is too high for those cordless alarms to be of any use -- you just can't reliably hear them.
Safety reins do not traumatize children; they are a safety device just like a carseat is, and if your child needs them to be safe it really doesn't matter whether or not he likes it. For best acceptance it is best to begin using them in public places as soon as a child begins cruising, so that at the age they are most useful, children don't have any recollection of walking in public without them.
For most healthy kids, age 3 is usually about the upper limit for needing reins to curb the darting impulse, though children with developmental or sensory issues may still need to use them at places like WDW when they are a bit older.
A properly adjusted rein will fall just to the tops of a child's ankles if you let go of it; it should not be long enough to hit the ground. This length is far enough to let the parent's arm hang at rest, but not long enough to create a trip hazard for other people by putting too much distance between the parent and child.