I like the idea of actual testing. Michael Crichton was said to have spent 1-2 years researching his topic before he even began writing his stories. If only every scifi author were willing to do that. I don't know if you have watched Mythbusters, but they would probably first do the experiment small scale and then do it for real in the ocean using some kind of conductive ammeter dummy to represent the marine organism.
So small scale could be a cup or bowl or 5 gallon bucket or bathtub. As Jim said, you can just get yourself a cheap multimeter. Rat shack has some cheapies, but I'd check out
MCM Electronics as well. They have what I think is their own brand of pretty decent budget DMMs branded Tenma. I have a Tenma DMM that has survived more than a decade of use and abuse. I notice two decent DMMs for $15, one foldable pocket size and one standard size. If you really can't think of any use for a cheap DMM you could always sell it on ebay or even return the rat shack one.
I'd start with at least a 5 gallon bucket. If you live near the ocean you could just drive down to the sea with your bucket and use genuine sea water for the test. Otherwise you can try to simulate it by mixing some quantity of table salt into it. The problem is it won't really be a fair test unless you can manage the right amount. You could do the 3% by weight thing, but you'd need a pretty sensitive scale to weigh the additional salt. I suppose a food scale would work. Those can be bought pretty cheaply I think. First you'd weigh the empty bucket. Then you'd weigh the bucket full of water. Then you'd subtract the empty bucket weight from the water and multiply that by 0.03. Convert to ounces or grams and then weigh out that much salt on your food scale.
So now that you have your bucket of real or pseudo-seawater you need a voltage source and a DMM which measures resistance and current. Ultimately what you want to know is the resistance per unit length of seawater and whether or not it varies in a linear manner as well as the amount of current that would pass through a somewhat conductive object in the water.
Note that running a current through salt water is also called electrolysis of aqueous sodium chloride. Normally this is done with direct current. Sodium, sodium hydroxide and hydrogen gas collect at the cathode (negative terminal) and chlorine gas and possibly oxygen (with enough voltage) collect at the anode (positive terminal). Your protagonist will probably be using an AC source (like a large genset) which means the anode and cathode will switch sides at the frequency of the generator.
Needless to say, this is an experiment best performed outside on a windy day. As a young child I connected a 6 volt lantern battery to a bowl of salt water in my bedroom and watched in amazement as a strange yellow metal collected on the negative side and a greenish-yellow gas was released on the positive side. Actually I think I may have been seeing if I could kill some insect by putting it in the water between the electrodes. I ended up calling a hospital to ask about chlorine gas exposure when I realized what I had done.
There are any number of possible voltage sources. You could use a cord plugged directly into an AC outlet, but I would start with a lower voltage. You could cut the end off an old AC adapter or use a 6V lantern battery like I did (are those still made?) or really any kind of battery with more than 1.5V. A 9V battery with clip on leads would be perfect.
The first thing to do is not electrolysis though. Just set your multimeter to read resistance and stick the leads into the water and write down the measurements for various distances between them. This information is useful in terms of how far away from the animal your electrodes can be and how much that distance will diminish any current that might reach the animal. But what you really want to know is whether any current will flow through the animal at all.
There are a couple ways I can think of to do this experiment. The first is with an artificial animal. The problem with this is that you need to know the resistance from one side of the animal to the other. You could go to a fish market and buy a salt water fish, preferably a large one. Maybe a swordfish or tuna steak, but you don't want a fillet. You want a cross section of the fish with the skin still on. Skin has a huge effect on the resistance of an animal. So if your marine animal doesn't have scales this may not work so well. Anyway use your multimeter to measure the resistance both on top of the skin and under the skin at the longest distance you can. Ideally the fish skin will be completely dry, but if it is wet it needs to be fresh water. Otherwise the experiment won't work. You might also be able to use a fish steak to test for current with voltage in the salt water bucket, but you'd have to figure out some way to make sure that no metal from the multimeter leads was in contact with the seawater itself. So that probably wouldn't work. Once you know the resistance per unit length of the animal you can try to build some kind of floating object with similar resistance and with metal leads buried in it that can be hooked up to your multimeter to measure the current flowing through it.
Alternatively you could use some kind of actual live animal. Personally I don't think you will be able to harm the animal at all unless it's a land animal that drowns or a sea animal that is injured by the chlorine gas or sodium hydroxide. Not even with 120 volts AC. But I could be underestimating how good of a conductor the animal is and how poor a conductor seawater is. The obvious option would be a live fish. You could keep it in the center of the bucket with a net or let it swim around. It would be cool to have an adjustable voltage source so that you could see if the behavior of the fish changed at all as you raised the voltage, but for starters you could try plugging in your 9 volt battery or whatever and see if the fish continues to swim normally. I don't think the fish will be bothered at all by the electric current, but will eventually be bothered by the sodium hydroxide slowly settling at the bottom.
You could also use a lab mouse (can be bought from pet stores), but you'd have to give him some way to float because mice can only swim for about a minute before they tire and drown. As with the fish you might put the mouse in a net and suspend it so that only the bottom half of his body is in the water. One way to decide on the type of test animal is based on the type of skin your animal has. For scales use a fish. For a shell use a crab or lobster. For fur or bare skin use a mouse (you could even shave it). So what would you be watching for? Any obvious changes in behavior when you turn the voltage on or obviously their death would be a significant result.