I did that same job a while back. Yah, they don't make it easy.
My experience is that the tolerances is so tight that there is hardly room to get a tool in there in the first place. So tool selection is likely the make or break deal here. Assuming that you are dealing with the same thing that I found, that is.
In my case, the two halves were not chemically welded together, they were pin and tab snap together. As I say, the tolerances were so tight that few tools would do the job correctly. A regular screwdriver (even the smallest regular one) was basically hamfisted. An Xacto knife was too weak for the job.
What I ended up using are what I call Jeweler's screwdrivers. Probably not the right term but the ones that you buy at electronics stores for getting to those really tiny ones. They are both hard enough and small enough for what I did.
After that, the issue was not knowing where the tabs actually were. If you can get the actual specs, you can probably go after the tabs directly. What I did was to probe the edges a bit to see where I got the most flex and took that to be the center point between the tabs.
When I was done, the result was not pretty but it worked. Since a laptop battery is invisible when in use, that seems to be a minor consideration.
Also, you say that you have already bought the new batteries. You might want to rethink that if it is not too late. I have rebuilt a few battery packs over the years and if you know the specs that you are looking at, you may have room for an upgrade.
The crown for me is an old hand held scanning radio which is on its third set of batteries. Each time has been a large change in capacity.