Without referring to any manuals (off the top of my head).
Generally RPT operations require a guarantee that we can accept any major failure, and still continue operations to an airport. E.G.: if we lose an engine at any point in the flight, we calculate that we have the performance required to avoid terrain, and the fuel needed to reach a destination etc etc.
So - loss of the oxygen system requires a descent to 10,000 - in the same way that loss of an engine (in a twin) requires diversion to the first acceptable airport - as you no longer have redundancy for a failure.
Once you are at 10,000 - where you can motor to depends on how much fuel you have. There isn't any need to divert
per se (in the sense that everything else is working), but your remaining range is obviously going to be curtailed (and you can't fly over high LSALTs).