CNNs - Hyperparameter tuning with different training sizes of the same data set
First suggestion: you should first find a CNN architecture that satisfies you, and then stick with it.

Second suggestion: be careful with cross validation. CNNs are extremely "heavy" models, they can easily take hundreds of thousands or millions of trainable parameters. Running cross validation on those could be computationally impossible.

In other words, keep the two problems separated.

I suggest you to take a look at common CNN architectures. There's plenty of them on Kaggle competitions (for MNIST, Fashion MNIST or any other dataset). You can choose one that works fine, and then use it to show how much the classification performance (test accuracy) of CNNs changes depending on the size of the data set.