Hardwarz,
I'm not sure what amperage the hazard light fuse is, but the strobe supply may be too much power for the fuse to handle. Also, you would have to be sure to wire it before the relay, so it gets constant power, instead of alternating (like the on/off flashing that the lights get).
As for strobes, Whelen is your top brand, in my opinion. My strobes are about six years old, used frequently, and are still the originals.
Of course Whelen power supplies are also very good, but I've worked with SVP power supplies also, and have never had a problem from them (and they're a bit cheaper).
Good luck with your project!