Just before you are getting ready to fish, go into your options screen (Esc) and choose Controls.
Now change the left camera to "Z" and the right camera to "C" - or whatever keys you want to
assign to them. Left and right arrow keys work as well. Don't forget to hit "Accept".

Now when fishing, use your mouse buttons as usual, but use your new keys (Z and C) to
counteract the fighting fish.

When done fishing, go back into your options - controls and hit the "Default" button to switch
your controls back to normal.

That's it! Hope this helps someone as much as it helped me.