What are battery replacement options for the Olympus OM-1?
Use the WeinCell MRB625 replacement battery for PX625/PX13. This is designed as a drop-in replacement for the OM-1, and even says so on the packaging.
Get 1.3V hearing-aid batteries from the drug store. Apparently they fit and work.
Use readily-available 1.5V lithium cells, but learn to read the meter as off or trick the camera by setting the ISO down by two stops. (That is, if you're using ISO 100 film, set it to 25; if you're using ISO 400, set it to 100.)
Get an adapter which converts 1.5V to 1.35V, like MR-9 Battery Adapter for Film Camera & Exposure Meter.
Have your OM-1 overhauled to take modern batteries.