Here's a bit of info that may prove useful.
Sub Nuke officers are almost always locked into Nuclear billets, even for shore duty.
Surface Nuke Officers, over a 20 year career, will actually spend a majority of their career in non-Nuke billets.
The surface fleet has far more non-Nuke ships than it does carriers, so the need for Nuke SWOs filling non-Nuke billets is very high.
EVERY long term (more than their initial obligation) Nuke SWO I worked with or for in my 20 year career had more non-Nuke assignments than Nuke.
Best of luck!
I'm not sure what you base this on...
On my shore duty slate, there were about 6 nuke jobs (4 prototype instructor, 2 power school instructor). The other 30 or so jobs were non-nuke billets; subschool instructor, trainer instructor, staff at X command, NROTC instructor.
If you one is a NAV/WEPS, it's difficult to get a shore duty that is a nuke billet since they usually want a served ENG.
It is true that at sea in the sub service, the nuclear power aspect never goes away. As a Nav/Weps, you'd be expected to maintain proficeincy as EOOW (which amounts to standing just two watches a month in the ER) and participate in the eng dept training program because you have to be able to perform as the Eng if anything were to happen to him. As an XO, you are responsible for the entire crew including the nukes, and as a CO you make a lot of the bottom-line decisions regarding the operations of the plant.
The thing I've heard SWO(N) complain about is brain-dumping all the nuclear knowledge after their carrier tour in the process of doing their shore tour and non-nuke DH tour, but then they're expected to be experts the moment they show up to the carrier as a DH.
That is what I have found from browsing the internet. The false rumors that SWO(N) "sucks" "isn't real nuke" basically all the generalizations lie in that a SWO(N) will spend just as much time as a SWO; which is just about preference more than actual experience I suppose. I want to do nuclear. That settles that.
Just to clear something up...
Those gold dolphins you are going to qualify for are not about the nuke plant; they're about tactics. The sub doesn't exist as a training platform for nuclear operators. The nuclear operators exist to allow the sub to go on missions it couldn't do on diesel-electric power. Your primary job as a sub officer is to develop into a CO capable of getting the ship where it needs to be and putting warheads on foreheads. Some of that includes learning about and supervising the operations of the reactor plant; most of it does not. The officers who spend their entire JO tours in 'the box' often feel like they missed out on the action of being on mission.
Yes, all the officers on a sub sans the chop are nuke trained (except maybe the AWEPS on a boomer if you get an LDO). However, even if you are an ENG as a DH you will devote a significant amount of your time standing watch in the conn and doing tactical stuff... 6 hours every 18, in fact. You will have to participate in officer training which is usually about tactics. It sounds like you have this picture of submarines being little more than an undersea nuclear reactor plant.
The fact that the surface fleet splits it up allows you to focus on one or the other at one time, which generally gives you more free time to do something else. It's just as annoying for the ENG to listen to a JO fumble over torpedo pre-sets in a slideshow for an hour as it is for a Nav/Weps to listen to an MM1 regurgitate slides on heat transfer equations for an hour for the billionth time when you're on very little sleep and the XO is up your ass for who knows what.
Also, pertaining to the NRE/Sub officer, I don't think I am in the wrong for wanting to have an experience in the Navy differing from what waits for me in the private industry.
I hope you realize that there is an expiration date on your engineering degree. Most employers will want to get their entry-level employees from interns, but if you don't have a job lined up in your senior year you're behind the curve. If you don't work in the field for 5 years to be a sub officer, it's going to become more difficult for you to get back into the industry than if you had just gotten a job to begin with.