If no other races will so much as sell reactors, the only option for your bioroids is to find a
natural reactor on their planets.
That said, it's likely that most systems will have at least one gas giant, and those are excellent sources of ionizing radiation. The Juno probe's 2 week trip around Jupiter was an estimated 20 million rads, which is probably enough of a dose to "feed" even their largest vessels (assuming you either rubber science things, or give them a racial Reduced Consumption).
If the need for radiation is only for some form of chemosynthesis to create some sort of vitamin, just park near a gas giant or as close to the local star as safely possible, and all is good.