Plenty of people film and spearfish at the same time now days. Some people have brackets attached to the stock of their spearguns with a camera bolted on and others simply hold the gun in one hand while shoot the speargun with the other.
When spearfishing and filming at the same time it is easy to make the image on the camera "jolty". By using a wide angle Lens you can improve the stability of the video plus have more of chance of capturing the fish on film simply by increasing the field of vision.
The down side of using a wide angle lens is that the subject will appear further away and smaller that it actually is.
This short clip shows the difference between the two. The fish in this clip are really quiet large.