From what I can tell, the Optima 500 Sensor does need a battery to operate. Without a battery it won't be able to select an appropriate aperture/shutter speed combination and there seems to be no way to set it manually. (There is a manual bulb setting, but that's not much use for daylight pictures.)
Finding the correct battery can be tricky. However, you might be able to find a substitute. 1.35V zinc-air cells for use in hearing aids will, in fact, work perfectly and are very inexpensive. They usually don't last very long, but that's not a problem at their price. Their diameter is smaller than that of the original px625, though, so you'll have to make a little paper collar or perhaps use rubber bands to keep the battery centered in the compartment. That's what I use in my Rollei 35, which needs the same battery.
Another option are 1.5V alkaline button cells. Since the voltage is slightly higher, you'll need to compensate by setting the film speed a little lower (or maybe higher, I'm not sure). The voltage will vary over the lifetime of the battery, so your exposures may not be super accurate, but it's usually good enough.
I hope this helps. Let us know if you have more questions and have fun with the camera!