Are you pressing your strips or ironing? There is a big difference. With pressing you put the iron on the fabric and lift straight up, you continue this until you are finished. With ironing, you are moving the iron around as you would ironing your clothes. The big difference is with ironing you are moving your fabric around which will make wavy lines. With pressing you are not moving anything because you are picking your iron up, therefore no fabric movement.
I know you say you don't like to iron, but if you are going to use fabric spray, I suggest you use it before you cut the material.
On the internet there are lot of explanations on how to 'press your blocks and fabric'.
Good luck, hope this helps.
I was wondering the same thing about pressing vs ironing. Have you heard of and tried a steady betty?
Also, this video might help you get an idea of what's happening with your cutting. It could be you are not squaring up before cutting your strips.
https://www.youtube.com/watch?v=yI8kkFnpwpM