GoPro lenses are very fish-eyed. Unless the camera were to be consistently within about 2 metres of your son at all times the result would probably be quite useless...."That tiny, wee swimmer way off in the distance....can barely see him.....oh...he's only 5-10 metres away."
The new GoPro Hero 4 models do the field of view quite well. The sensor is a 12MP native unit, so at Full HD (2MP) this is down scaled significantly.
When you switch to Medium or Narrow field of view, they take a smaller segment, say 8MP closer to the middle of the sensor, and use this to scale down to the Full HD output.
Narrow is really small, closer to a 1:1 sample in the middle.
Noise can become an issue, because you're not getting the averaging benefits of a major down scale, but that may not be an issue at all depending on your use requirements. Also, pick a suitable frame rate, beering in mind the effect on exposure and motion blur. Higher frame rates give less motion blur, but require more light (or a higher ISO) to maintain the same correct exposure.
Point is, you can change the field of view on a GoPro without applying digital zoom. The resulting output is pretty good, and this gets away from that tiny guy in the distance issue.