Actually, there are quite a few Republicans and Democrats running for this seat.
This from the Alaska Division of Elections
http://www.elections.state.ak.us/cand08p.php:
United States Senate
Mark Begich (Democrat)
Bob Bird (Alaskan Independence)
Rocky C. Caldero (Democrat) - WITHDREW
Gerald L. "Jerry" Heikes (Republican)
Ray Metcalfe (Democrat)
Roderic H. "Rick" Sikma (Republican)
Ted Stevens (Republican) -Incumbent
Frank J. Vondersaar (Democrat)
Rich M. Wanda (Republican)
Although I don't see his name on the list, apparently David Cuddy is running for the seat as a Republican as well.
http://www.davecuddy.com/