It isn't hard to measure the shaft runout. Take less then a couple of minutes setting up a magnetic base dial indicator to the trailer, lubing the prop shaft, then turn the prop by hand and watch the dial move. You just have to be smooth as you turn the prop. Harbor Freight probably some cheapo crap dial indicator that would work for checking runout, or have a shop check it out for a half hours labor.
The reason the shaft needs to be checked is because damage to the transmission/driveline is expensive. Even if the boat feels smoother after the prop fix, the shaft could be bent and do damage.
Andy Z is dead on about checking the strut too. Remember on some boats the rudder can be offset.
With all that said, it is most likely the prop. Would your boats performance improve with a prop upgrade? Having a spare is never a bad thing and will get you back on the water this weekend.