My understanding (having gotten married last summer - though I bailed on having a shower) was that you only invite those to the shower that are also invited to the wedding. If you were invited to the wedding I'd say that you should send gift even though you won't be there. However, not being invited to the wedding you're probably only technically on the hook for a nice card and your best wishes.
If you do have a good relationship with this cousin though - and the available funds - you can always pull together a small bridal shower gift (go to their regsitry and pick up a handful of the small items - things like spatulas, wooden spoons, kitchen towels, etc - things that don't cost a lot) and send those along with a note. Or if your mom or your grandmother was also invited you could go in with them and buy something and then add your name to the card.