Forget about resolution, it's meaningless in this situation. It doesn't matter whether it's 72 PPI or 300 PPI. Just forget it. A crop ratio of 16:9 isn't that huge. It is the aspect ratio of your screen at 1920 x 1080 pixels. If you create a custom crop ratio of 16:9, and then crop the image, then export with the long edge of the exported image being 1920 pixels, it will be in the 16:9 aspect ratio and will fit your screen perfectly. I do this all the time.
Again, 16:9 isn't a "huge" aspect ratio. It just means that for every 16 pixels horizontal there will be 9 pixels vertical. And the export process allows you to specify how many pixels you want on your long edge or your short edge.