If you want to work in a laboratory setting, that's where you should apply as stated above. As an engineer at a shipyard, you won't be in a lab either, you'll be engineering controls into paperwork for the trades to execute as part of the build, overhaul, repair process. There are laboratories at the shipyards doing things like analyzing pure water, looking for detrimental materials, and conducting tests of products to ensure they meet MIL SPECs.
As an NR engineer, you won't be breaking a lot of new ground unless you get into the advanced projects section which is working on the next generation nuclear propulsion plant. You'll be working on stuff with the existing plants and ensuring the existing technical requirements are met.
But, with a little more research than you've done, I'm sure you could have found all that on your own.