Is it safe to rebuild my laptop battery pack?
As Tom Carpenter commented, "Just buy a new one. It's not worth the effort." 

First, you need to get unprotected cells, because the local individual protection circuitry will interfere with balanced charger built into the "smart laptop battery". 

Second, you will need a welder to connect new cells, reliable soldering would require either a low-temperature alloy, or careful temperature control, not to overheat cells. Unprotected cells need some care to handle, to avoid accidental shorts. You might need to deeply discharge the cells before handling-assembling them.

Third, and most important, you will need to match the cells that go to paraller (2P) connections to 1-2% in terms of internal impedance and capacity. Without matching the 2P sections will wear itself down rather quickly, in 50-100 cycles, and die. When the smart batteries are assembled by manufacturer, their factory has thousands of cells to select proper matches using special testers. You don't have this luxury.

"Just buy a new one. It's not worth the effort."