Hi Nizar,
I think you are getting hung up on the wrong thing. Yes, without the corrections, the SWR value will be a little bit off, for instance if you use your 75ohm cable to match to a 75ohm load (a dipole), you may get an SWR reading of 1.6 instead of 1.0. With your 56ohm cable the difference would be minor.
But in all cases, the lowest SWR (the dip in the SWR curve) will appear at the same frequency - only the value of the SWR will change a bit - so you can always tune your antenna without doing any of these corrections. Just tune for the lowest SWR dip. And yes, as Roger correctly pointed out, the minimum SWR is not always at the resonant frequency, but it is close to resonance in almost all cases, so tuning for low SWR will give good antenna performance.
Just use the nanovna as you have it, and you will be able to tune some nice antennas. The difference between a 56ohm feedline and a 50ohm feedline will be insignificant for all simple antennas - it will only become relevant if you are doing phased arrays using the feedline. And using a 75 ohm feedline will also be insignificant in the tuning of most antennas. And the difference between an SWR of 1.5 and an SWR of 1.0 is insignificant - the station receiving your transmission will not be able to tell the difference.
So go out and tune some antennas and have fun on the air - the correction factors you are seeking are only a tiny part of the performance of your system, and in my experience, not worth spending time on. I never use them.
Stan KC7XE