Completely agree with the points made by Axel Klein
The only other thing I would add is that sometimes you may need to use a buffer to help mitigate drastic changes in pH, stabilising the system. A buffer is not the same thing as an electrolyte, but may act as an electolyte in many instances.
When selecting a buffer you may wish to consider the useful pH range. You may find the following information useful:
It will have an impact on the reference electrode. The same is true for the solvent. That means if you want to compare potentials they should be ideally measured in the same solvent, using the same electrolyte with the same type of reference electrode.
The impact of the electrolyte can be reduced by using chemically very inert salts like (NBu4)(PF6) or (NBu4)(ClO4)
I cannot but agree with Jules Lloyd Hammond and Axel Klein .
In response to your last question, the electrolyte affects your CV measurements in the sense that the solution has an uncompensated resistance depending on the electrolyte species and their respective concentrations.