Hi Dinarius,
"Is there any way to just save the hexagonal shape I have selected and not a rectangular shape?" If I'm interpreting this question properly the answer is NO. I believe you want the "Canvas", which contains the image, to be hexagonal. To the best of my knowledge there is no way of accomplishing this is PS or any other app. If that is not the case I have never seen it or been able to accomplish it. And yes, the background will be transparent and it will still be a rectangular shape, not the hexagonal shape you want. But the easiest method is a compilation of both.
1. Create the selection.
2. Control or Command + J to save the selection to a separate layer.
3. Trash the Background layer - DONE
However, the selection will still reside within a rectangular Canvas.
Gary