I'm not entirely sure what the issue your having is, US Letter paper is 215.9mm x 279.4 mm whilst A4 is 210 x 297mm essentially yours is longer and marginally narrower, but since the dimensions of a printed dvd cover are 274.32 mm x 184.15mm the image you want to print will comfortably fit on either.
My advice in the first instance is to consult the manual of your printer and find aout the maximum imageable area, on a laser printer this will be smaller than the page size. On most modern inkjets you can turn on edge to edge printing which may fix the issue.
Printing from photoshop is pretty simplistic but here's a link to a guide for Mac and PC users which covers a couple of workflows for the colour management issues you may encounter (I chose this one because it includes swedish and english).http://www.computer-darkroom.com/ps9_print/ps9_print_1.htm
Hope this helps