What you’re thinking of doing is pretty similar to what I did.
If you crack open one of the original packs, however, you’ll see the cells are side by side vertically, and 16 total cells fit in.
So I bought these:
2x Exell Custom 9.6V 800mAh (8xAA) NiCd Battery Pack https://www.amazon.com/dp/B088G27D9M/ref=cm_sw_r_cp_api_glt_fabc_CE4W4R3CT8EY9975PYBK
Then I measured the original pack casing, rebuilt it in 3D, and 3D printed a new casing for it. I can share the design with you if you’d be interested. (Possibly print you some too?)
For the type of batteries I bought, soldering them in series was the hardest/scariest part, because I had to solder leads to the battery contacts themselves, which is potentially dangerous. If you can find a pack that has leads coming off like in the link you showed, that would be safer.
I soldered the leads to little crimpable metal contacts that I hot glued to the openings where the cameras pins enter the casing. Hot glued all the cells in, hot glued the case cover on. Voila.
I can add pictures of the finished product when I get to my camera (currently displaced due to Hurricane Ida). Also if I make another pack I can take pictures of the process a bit more possibly.