I'd be more worried about oil in coolant then coolant in oil, the effective flushes are solvent flushes. Kreen by kano is pretty much accepted as a top flush, so harsh you cant buy it in some places. You can probably get away with most flushes you see on the shelf, likely similar science as in solvent cleaner. I'd be on the fence to flush or not to flush, I'd be 50/50 on that decision whether to flush or just use a cheap oil for 100 miles or so and dump. If you see a flush you want to buy, look up the msds for solvents and see %. Solvent flushes work, personally I would run them for many many miles, but some people do. The risk is the oil filter clogging up. If you run a flush, do it now in old oil, dont change the oil just to flush it.
Now, for the radiator, if any oil got in there, rmi 25 for sure, it will take any oil and trap it in overflow tank, the stuff is amazing and safe.,