Hi,
you want the best solution.....but you don´t say what "the best" means for you.
For the one it is: The cheapest, the smallest, the lowest power consumption, the easiest to build as one piece, the easiest to build for millions, the one with lowest software effort, the one with lowest hardware effort, the most light weight solution, a water proof solution, a solar powered solution....and so on.
I guess you dont get a solution to fulfill all of your (to us unknown) requirements.
Basically you need some timer. Many ways to do. Mechanically, discrete solution, microcontroller solution, a cellular phone app, a PC, a PLC, internet ...
I guess the fingerprint reader is conneted to some device. We don´t know what this is.. maybe we can use it as timer, maybe not.
Without detailed informations from your side we can imagine a book full of solutions....with huge effort on our side, but only a tiny use for your side.
Klaus