The special No More Heroes site has a little more information about Travis Touchdown and few screenshots to see.
Travis’ primary weapon is the Beam Katana, which he won from an online auction, but he can also fight using wrestling moves.
The Beam Katana can block bullets.
You need to keep the Beam Katana charged by picking up batteries and if you cannot find any you can power the katana by shaking the remote.
If Travis gets stuck in a swordfight you can rotate the remote to push an enemy’s sword down.