Pete,
I have the Honda S2000 start push button. Not that, that information is relevant. What is, is that on my schematic(which I didn't wire into my car) there is a clutch safety switch in line and its principal of working is the completion of a circuit to ground from the relay that supplys the power to the starter. Ratings of any switch are listed as their max carrying capacity. This is usually there about, 20% over what should be flowing. Maybe off on that number, but you don't want a spike over that rating, or it will/could fry the switch, leaving you stranded next time you try to start the car. If what you are stating is the true amperage then you will probably be O K. I just wouldn't want to take a chance. A safety switch is just that. Not one that should carry the load. I have several safety switches on my car. One of the biggest is for my fuel pumps when the oil pressure falls below 15 psi. When it does it cuts the power to the pumps which is their relay ground wire not their supply power. The relay will do that. When starting the car I have a bypass switch that allows the pumps to run during starting.
Bill