Push button starter switch with a relay

Looking to install a push button start on my riding mower with a relay so I can use a basic push button instead of an actual starter or horn push button. I figured I could use the wiring at the starter solenoid. I want the relay because the push button I want to used won't handle the voltage or amperage. I will still be using the key switch to turn the mower off, so in the on position the push button will start the mower. So any help would be greatly appreciated

Neg to push button then push button to 85 IGN to 86 20amp constant (use ignition switch feed) to 87 30 to solenoid.