use battery to generate weak electric field?
There are two main problems with creating a known stable electric field in sea water to see its influence on marine animals.

1) When a current passes through sea water it changes the chemistry. I would wager that sea animals also respond to the gradients of chemicals that would be released by the action of the current just a strongly as to the electric field. It's a major part of the experiment design to separate the two effects.

2) The voltage measured between electrodes and the sea water depends on the electrode material (think battery), and the recent history of the current that's flowed in or out of the water in the vicinity of the electrode (in batteries, this is called polarisation). As the current flows, and as time passes, the polarisation potential changes. This means that what you measure on the electrodes could be a volt or so different from the potential in the free body of sea water. Trying to establish what the electrical field in the water is, to \$\mu V\$, using measurements at electrodes that could be a varying volt or so wrong, is clearly doomed.

It's going to very easy to poke a couple of wires from a battery into a test cell and see animals react. It's going to be very hard to do it in a way that's reproducable, especially by others. 

I think your best bet, even for a 'quick look see', will be to use a 4 terminal setup (look up Kelvin connection). 

Use a porous pot, or similar semi-permeable membrane, submerged in a larger vessel. Your animals and sense electrodes go in the pot. Your drive electrodes are outside the pot. This will isolate chemical changes at the current carrying electrodes entering the experimental area. 

Sense the field within the pot with an identical pair of non-reactive electrodes connected to a meter. Platinum electrodes would be good and reproducable, though stainless steel, nickel or carbon might do for an initial test. 

Drive the field with a pair of electrodes outside the pot. Similar considerations for electrode materials, though they don't need to be identical. Initially, an adjustable lab power supply will be all you need, keep adjusting it by hand to keep your sensed field constant. Later, you can add a feedback amplifier to drive the electrodes to keep your sensed field constant. The amplifier is the easy bit, come back here once you have the rest of the setup going, and we can help you with that.