Can I make the showcase slider type to have different sized slides?

No, you can't. Our showcase slider because of it's system can only have the same slide sizes, so with different ratio images the only options you have is the fill mode options, that you can either make your images to cover the whole slide with the Slider background fill mode - fill option, or you can make them show the whole image with the "fit" option, but that leaves empty spaces around these images.