I don't really care about the speed with which the spear leaves the speargun as a number but I thought the following was brilliant.
Quote from wkittoPut a cheap microphone into a condom --- tie it off so the mic doesnt get water in it. Connect the mic to a laptop and put it (the mic since you still may not be thinking) into a pool where the gun will be shot at a wooden target suspended off the bottom by strings to your weight belt. Accurately adjust the distance from the end of the shaft to the target (15 to 20 ft for example) and with the computer recording shoot. Review the digital image of the sound in a sound editing program to measure the time distance from the sound of the mechanism and bands going off to the impact of the shaft at the target. From that point with a little engineering help you ought to be able to figure the average velocity over the distance traveled.