mark, i do not think that this would be a great idea. the problem here is that your iPad was submerged. The LI-Ion batteries do not like that at all. LI reacts with water and are essentially pretty dangerous. Also, there is more to those batteries than just holding a charge. They do have a "brain" of their own. So, you may have some problem with the circuitry of the battery. My suggestion would be to clean the iPad using this wiki as a general guide. After that, reevaluate and if you still have those issues, replace the battery.
Now, on the other hand, if you are really inclined in trying it out, there is a way. Since you already measure the voltage of the batteries, you do know the polarity. Here are the schematics for you to look at. These are charging circuits build to work with Apples "interesting" charging circuitry. Also check the pinouts and read the descriptions about the circuitry on here for further ideas. Once you have it build, connect the PCB contacts to your battery via alligator clips. Again, messing with LiIon batteries is potentially dangerous, literally explosive so I still recommend a new battery. Hope this helps to get you in the right direction. Good Luck.