AP9211 battery protection
There is no problem initially connecting P- to BATT- as this IC needs to short those two terminals to begin operating if there is no charger connected. From Page 2 in the Notes:

For  power  down  mode,  when  first  connecting  AP9211 system  board  to  the battery,  it  is  necessary  to  use  charger  or  to  short  P-  to  the  battery  negative  polarity.  Once  the  AP9211  is  activated,  the  charger  or  connection  can  be  removed,  otherwise  the  battery  cannot    discharge current through system board.

Edit:
You should connect BATT-, VSS and S1 to your circuit GND. It is my understanding that you can leave P-unconnected and floating if you do not use the charger side of the circuit and the protection side will still operate as per your use case but you should still check that yourself to confirm.