I've used a bunch of different tires that were not designed for the Hayabusa on tracks days and high speed runs with no problems. Many other's here have also. If you are not a canyon carver, track day rider or high speed freak, almost ANY tire will work perfectly for you.
In my opinion, the HPX rubber compound is too outdated now compared to the newer stickier and yet, longer wearing rubber they have developed from MotoGP experiences. I found the HPX fine at high speeds, and a little heavier, more rubber on them, but they were slow to warm up - slippery to me for the first 10 miles - which means I already got where I'm going before they heated up. So, that was no fun. I like the sticky feel of the Pirelli Diablos but, they wear fast.
I have not noticed any advantages to running tires designed for the Hayabusa - maybe a tad smoother above 170mph - but I don't see that speed often enough to warrent the purchase.
You will get TONS of advice from people on tires. I, personally, prefer stickier over long lasting becuase I want to BE ABLE to do everything very well, at any time. I don't want to feel restricted: "Oh, I can't rail around this corner because these tires wear better than they stick" That is just me.
So I recommend:
Bridgestone BT014, 15
Michelin Pilot Powers
Dunlop Qualifiers
Pirelli Diablos
Metzeler M3
Others here run Continental, Avon, Shinko and seem happy with them.
I'm also not a fan of running "race" tires on streets due to the need for harsher heat cycling and lack of pothole/surface protection. But many here run them just fine.
More fun reading info:
http://www.sportrider.com/tech/tires/