In a pinch, a wired doorbell button from hardware store will work. About $7.50 for a cheap one, make sure it's wired version as wireless wouldn't be easy to use
tomytronics
I rate this 3 turds. I would have rated 4 turds had you used different colored tape that clashed with red motherboard, maybe lime green?
And a mosfet between Arduino and the fan. Arduino generally tops out at 20mA per pin which is 0.1w. A decent mosfet can handle several amps and can even drive 12v fan from a 5v pin.
/r/AskElectronics should be a good place to ask for the right kind of mosfet that is able to handle 1A or more (want to have some margin), can be driven by 5v at gate pin and can handle 12v at source and drain pin.
I've taken apart a few old laptops. Most of the fingerprint reader is an entire board and circuitry in a small package with 4 conductor cable to the motherboard. If it is USB, OP could shove a fingerprint scanner inside the mouse but OP would also need to add an USB hub to connect the mouse and fingerprint reader to one cable going to the computer.
EDIT: disregard below paragraph, I missed the part about wireless. I've never seen a wireless fingerprint scanner
Not hard to do though, it depends on how much space is inside and how careful OP can be for wiring them up and mounting the reader so it can read without making ugly cutout
Keyword might be "contact paper" Clean the glass, apply clear contact paper as flat as possible, then trim the edges. Cover both sides to catch any small pieces that may try to escape.