In the past, I built a lot of batteries with these cells to experiment with my spot welder before getting into larger packs. Once I had welded a bunch of cells, I had to take them apart again and re-use them, so here is what I did.
A couple of things first, as others have said, water is not a good idea if the cells catch on fire, although what is more likely to happen if you do anything wrong (like touching across a don't touch zone with the pliers) is that you will get a big spark and the accompanying sound will scare you enough to pull away. If you can, heat-shrink your pliers' legs leaving only the tips exposed, that way, it is harder to touch across plates when you work. Safety glasses are a good idea as well.
In the battery you are trying to disassemble, notice the continuous sheets of nickel - as you probably know, these connect the negative of one cell to the positive of the next. What I would do, is put the tip of the pliers under the spot welds and push down on the pliers so the tips are pushing the nickel strip away from the cell, much like using a crowbar to dislodge something, or using a hammer to pull out a nail. If the welds are good, the nickel will tear and it can be separated by the cells, probably leaving some nickel on the cell. That's perfectly fine. If the welds aren't good, the nickel will just snap and separate. Either way, keep doing this, i.e., use the pliers as a crowbar and pull/tear away the nickel from each cell. As you do that, roll the nickel sheet much as you roll the top of a can of sardines till you have removed an entire nickel sheet. Be careful towards the end to make sure it doesn't touch the adjacent sheets - if you have a good pair of sheers, you can also cut it away once it has detached from the cells. In fact, for the cells at the top of your photo, where they are adjacent to each other, I would probably just cut the nickel with sheers then separate it from the cells with the pliers.
Once you have a nickel sheet removed, flip the battery and do the same but this time, hold each cell as you pry away the nickel strip on the other side. That way, when the other side of the cell is free, you are holding it as opposed to it rolling away. Put away each cell as it becomes free, cutting the nickel strips if they get big.
Once you have disassembled everything, you can use a Dremel to carefully grind away any remaining bits of nickel that remain attached to the cells. This is definitely not a standard procedure but it gets easier as you do it. If the Dremel runs away from you and cuts away the insulation of a cell (there may be a spark, don't ask how I know), resist the urge to keep it - that cell is probably best to be recycled properly.
I've taken enough of my "test" batteries apart that way, some cells multiple times, and it works for me. Hope it works for you as well.
