Use a 60 amp Bosch-type relay to activate the solenoid, and use the 1-wire push switch as a ground for the relay coil. Since the 60 amp relays are a little hard to find, two of the more common 30 amp relays could be wired in parallel. The pull-in winding on the Delco starter solenoid has a momentary current draw of around 50 amps, which will burn out a low-amp relay pretty quickly. Once the hold-in winding activates the current draw drops to about 10 amps.
Edit: Just looked at Ebay, and there are dozens of the 60A relays available at around $3.50 apiece. Most of them come with the appropriate wiring harness plugs, also! I think I'm going to stock up on those things, since they can also be used as fog light or horn relays, Borg-Warner overdrive controls, etc. Just search "60 amp relay" on the Ebay site.
Jerry