The two charge regulator ICs are the same except for the status pin #1. The ’31 has a tri-state output which can indicate “charging” and “finished charging”, the’32 has an open drain, which is low when “charging”.
If you understand detailed FET specs, any P-channel with the right specs (like the one inside the Fairchild IC) will work. The same applies to the Schottky Diode. The Fairchild combination is optimized for this application, small, and inexpensive.
Perhaps you are not getting the full picture, though. The PCB must be changed or modified by cutting traces and adding jumpers. Just adding the missing IC is a waste of money, because it is bypassed by the Diode. If you remove the diode, then the scope won’t run because of the low voltage due to current limiting while charging the battery. That is why the diode was added, but since this bypasses the charging IC, there is no point in installing it.