For anyone looking to get an idea of what Ryu Hayabusa could do, here's a bunch of his hand to hand stuff in DOA5. Though obviously, he'd use his sword from the Ninja Gaiden games and some of his Ninpo and Shuriken/Kunai too.
I thinking the Slide Kick, that Triple Kick, Sweep Kick, Dive Kick and Elbow would work. That throw where he stomps on you would work for a Down Throw. And again, Izuna Drop's gotta be the Up Throw, make it a kill move too. Maybe have it do more damage if you pull off the 360 motion before the end of the attack.
EDIT: Ryu also has a launcher kick that's similar to Nina William's Geyser Kick from Tekken. I think that'd make for a good Up-Smash.