I was able to locate the specifications online for the Lawrance/Simrad Pump-1. The Pump 1 can draw anywhere from 5.5 to 11.5 amps. The Navpilot 300, can handle 10 amps continuously and 20 amps for 5 seconds. So it would work but too be safe, I would put an inline fuse for 15 amps to protect the Navpilot 300 processor.
Is this Pump 1 existing pump on the boat? If so, how does it steer?
Then normal power usage of that pump is 5.5 amps. Being a "type one", it is one of the smallest. The Navpilot 300 should have no problems using it. I agree Kicker, I would fuse the pilot for 15 amps and rock and roll.
I don't see an issue with the information I was able to cross reference with the pump and our processor. Just make sure to add an inline fuse of 15 amps to protect the Navpilot 300 processor.
As long as it steers good now, I would proceed with the purchase of a Navpilot 300 with your existing pump.