Many games allow you to rebind actions to joystick buttons, so I'd check first and see if your joystick's D-Pad isn't already natively supported by Skyrim.
If that's not the case, or the options are limited, my go-to solution for these sorts of joystick and keyboard rebinding solutions is AutoHotKey. I've got some good links and a really short sample script over in this answer that might serve as a base.
You'll have to determine which joystick buttons correspond to your D-Pad, and then write a small script like:
Where A, B, C, and D are the numbers of the D-Pad buttons, and 1, 2, 3, 4 are the keys you want them to be mapped to.
You can edit this as you see fit, and save/run it as noted in the answer I linked. Then you should be able to use those buttons to do whatever it is you want in Skyrim.