Minus a specified course of training would passing the DOE Core and taking HAZWOPER be enough to get an entry level position?
Contact SEC or DeNuke for information on Rad Tech positions in the Oak Ridge area, but yes both Core and Hazwoper would be helpful if there are openings. Typically if you can survive two years at Y-12 as a Rad Tech you will likely be offered a house job by B&W (usually), not many Jr's hired, but occasionally they are, and the only way to know is to contact them.