Big Island Mike makes Joe go fishing for six Ulua fish. The first fish you catch is always an Ulua. The last fish you catch is always an Ulua, too. Other than that, "what fish you catch" appears to be random.
I figured this would be a good place to abuse save states. You know, make it so that Joe catches six Ulua and ten three-dollar fish. That way, Joe can trade in the fish for snorkeling equipment, without the need to make necklaces or go fishing a second time.
I tried it out, and guess what? The programmers thought of that. I made $28 in spare fish, and the game stopped letting me get more fish. Every fish I caught after that was an Ulua, which you don't get any money for. So it's impossible to make enough money for snorkeling, the first time you go fishing. That's probably because you have unlimited bait, the first time you go fishing.
The game glitches, if you go fishing without talking to Big Island Mike about Ulua. In order to do this, you have to make enough money in necklaces, to afford bait. The magical, unlimited bait appears if you do this, because you're fishing for the first time. You can probably get $30 from fishing, by using that glitch.
I also tested out the shells in the game. I can't figure out the pattern. It seems like they appear randomly, in real time. You can save the game, wait on the title screen for five minutes, then reload the game. You'll probably get at least a few shells like that. So in a speedrun, you could totally abuse save states to get all the shells you need. It takes a long time, in real time, but in terms of actual gameplay, it's not so long.
Which strategy is faster, though? Making necklaces or catching fish? Let's see. It took me 21.88 seconds to make an aloha necklace, which is $4. It took me 15-20 seconds to catch a fish, the most expensive (non-Ulua) fish being $3. So...yeah. Fishing wins, but it's almost the exact same amount of time. Like I said, you can't get the $30 you need, the first time you go fishing. Therefore, you'll have to fish and make one necklace. That's faster than fishing twice, because in order to fish a second time, you have to pay for bait, and you have to fish a few times to cover the cost of that bait.