I don’t want to have to buy an amp either. In boat speakers. Powered by head unit. when up loud enough for the surfer to hear they sometimes start to crack depending on the song.
Your experience with distortion can very well go hand in hand with NOT having external amp power. Head units are historically very week in rms wattage and most tend to tun a full-range output. When turned up loud, you can easily get a clipped signal and distortion.

An external amp will supply a more powerful, more stable signal to the speakers. This not only allows then to play louder, but sound better when louder.

So I would highly suggest investing in an amp to power those new speakers. Even then, you are asking a lot for an in-boat to project outside of the boat while under way, so to be heard by a surfer.