No alternate destination when flying from Oakland to Honolulu: is that correct?
There are plenty of alternative airports in Hawaii, but none in-between of course. So what the author is getting at is that you're probably going to be dead if you run into trouble.

While I can't say I know anything much about the Cessna 402, it apparently has a normal range of around 1,273 nm (1,467 mi, 2,360 km), compared to a distance Hawaii-Oakland of 2050nm (2359mi, 3797km). Hence, you're going to have to install additional fuel tanks and fly pretty heavy. 

There a few considerations if you get a problem: 


You will have to descend since the engine can't generate enough thrust at that cruise altitude. I found a source stating the ceiling for both engines is around 26180 ft compared to 11320 ft for one engine. 
The fuel consumption increases in the remaining engine and will be greater than the total for both engines for the same flying conditions.
You're going to have to run the remaining engine hard for the remain of the flight.
If your temporary ferry tanks screw up (or any of the normal ones for that matter as well), you won't make it.
You may damage/break the gear if you have to return to the airport overloaded. "I once saw a Cessna 402 parked on the ramp at Honolulu with the gear punched half way up into the wings from a poorly executed overweight landing." Source


I can't do a calculation on for what portion of the flight you would be 'screwed' but I imagine it might very well be a bit of the journey. Several people seem to be in the opinion it's a pain to fly heavy and difficult to with one engine.