Caution
While your idea is a good one you need to proceed with caution.
The cells are usually joined by metal strips that are spot welded to the cell. Do not attempt to remove the strip. By doing so you risk ripping a hole in the cell which will damage the cell's operation. It is best to cut the metal strips and rejoin cells via the this strip.
It is NOT recommended to solder directly on the cell as the heat can cause damage to the internals. If you have access to a commercial battery repacker then I suggest you take your sorted cells there and have them joined via welded metal strips. These guys repack battery packs for all sorts of things like cordless drills, laptops etc. So they have the right gear to make the best joins.