Most alarm systems run on 12VDC - looks like yours does. If that’s the case, you could rewire the alarm loops to draw 12V from the alarm panel. Then use a converter at the far (camera) end to get 5V. Rick suggested one such device.
Another is this one:
There’s a category of such converters intended for powering dash cams and other automotive accessories. You’ll find lots of them on-line. They generally come with either a miniUSB or a microUSB cable. For the Wyze cams, you want the latter.
To minimize power loss across long runs of alarm cables, it’s best to twin the wires. It’s common for alarm installers to use ‘quad’ (4-conductor) cable: one pair powers active detectors, like your motion detector. The other pair is for the alarm contact. If you twin the wires (use red+yellow for the positive, and green+black for the negative), the wiring resistance will be lower. Hence less power loss.