To answer your question, you can do it either way, but as has been noted - if you're using the original push button switch, keep the solenoid, too.
If you rewire it, using the switch that's supplied with the SeaEra, you won't need a solenoid because it is a heavy-duty switch.
In the original case with the Crown Head II, the switch is only rated for about 5 amps and will burn out in short order if a solenoid isn't used with it, to carry the heavy motor load.