Image size doesn't work because you can change only height and photoshop automatically changes width to match the aspect ratio so that doesn't work.
You don't have many choices here. If you want to change to an image size that has a different aspect ratio you have to crop. If you want to change the image height and keep the aspect ratio the same (no cropping) you have to except the image width that goes along with the aspect ratio.
If you MUST have a particular image size with a different aspect ratio and you CAN'T crop, then you would have to stretch the image in the vertical or horizontal dimension, but I can't imagine when that would be an acceptable solution.