Both of what you have suggested gives an unbiased estimate of the test set error, which is the most important aspect.
But your second approach has probably lower variance error, since you are also switching up the validation set.
But keep in mind your procedure differs from cross-validation and I also would not call it that way, or else you are confusing people.
At least in your second approach, I can tell what you are doing is nested resampling, where the outer resampling is cross validation and the inner resampling is holdout (see here 1 for more)