CR123A Battery Holder Picatinny Mount. Can mount to a real one to one scale of picatinny rail. Use #10-32 1-1/4 inch length Socket Head Screw and #10-32 Nut. Use a ACCO Jumbo Paper clip Stock#72580 for hinge.
#10-32 1-1/4 inch length Socket Head Screw
https://www.fastenal.com/products/details/24045?term=%2310-32+1-1%2F4+socket&r=~|categoryl1:%22600000%20Fasteners%22|~%20~|categoryl2:%22600039%20Sockets%22|~%20~|categoryl3:%22600043%20Button%20Socket%20Cap%20Screws%22|~
#10-32 nut
https://www.fastenal.com/products/details/0149142?term=%2310-32+nut+black