Sunset's not used to fighting such bizzare monsters, considering his time period, but it can't be any worse than a gigantic villain with a gatling gun, can it? Regigigas is slow. Not only that, but its damage is terrible for five turns thanks to Slow Start. That means that Sunset has all the time in the world to do whatever he wants. Hurricane Shot should outright kill, if not seriously maim, his opponent, and while usually the three turns it takes to execute makes it completely useless, here it's exactly what he needs. Of course, Regigigas's paltry attacks are nothing to worry about, and there's nothing it can do to avoid a Hurricane Shot. Speaking of avoiding attacks, even if Regigigas manages to launch a few attacks on him, Sunset will probably evade at least some of them anyway! With all this in mind, Sunset definitely has the edge over his Poke opponent.
Regigigas isn't much of a gunslinger, but it matters not. Sunset has no way of immuning Confuse Ray, which will buy the King of Regis enough time to shred its crippling disadvantages given by Slow Start. Regigigas's attacks, while initially weak, will still cut through Sunset's terrible defenses like a knife through butter, and its own natural tankiness can absorb plenty of punishment while it slowly whittles away Sunset's HP, should the cowboy break through confusion. A few Mega Punches here and there and Giga Impact for a finisher will hopefully end the fight before Sunset can pull off a Hurricane Shot. And should the battle happen to last past five turns, Regigigas will be free to unleash its full power upon Sunset and easily destroy the frail gunslinger. It might not be short, it might not be pretty, but Regigigas can win this fight, and with any luck, he will.