Didn't we tell you already that was a bad idea when you wanted to do this with a Balao? You'll never get more energy out of the graphene moving through the water than it takes to push the ship through the water. Better to just use a conventional engine.
As for the smuggling, you're best bet is going to be a sub with electric engines. If they run on batteries then you're going to have a surface or run shallow and snorkel every day or couple of days to charge the batteries and swap air. Additionally the hull will ring like a bell on active sonar unless it has some sound absorbing skin. This won't completely eliminate the sound of the sub but if you're running ducted turbines on electric motors the squirty water sound combined with the soft skin may mimic the sound and return signature of a biologic (a whale) and fool a green sonar operator. You'd need to operate the ducted turbines in pulses and match the frequency of the pulses to the tail strokes of something like a blue whale but it could be possible.
The big problem with a soft skin is that it will want to cave in at the front and this will cause additional drag and slow the sub significantly so to move at speed while submerged you'll want to be able to push some hard plates out or fill bladders with pressurized sea water to brace the skin. This will largely negate any sound deadening characteristics of the skin but give you a boost in speed.
The other big problem with soft skin is that it will limit the dive depth. Go too deep and the hull-skin will cave in and tear open. This happens on steel and titanium hulled subs today and if you've ever been in a sub approaching its rated crush depth you might have seen the inner hull bow in visibly.
For armament skip the railguns and just use torpedoes. Early subs were armed with guns because torpedoes were expensive, unreliable, inaccurate, and difficult to aim and fire. That's no longer the case and there are now a variety of long ranged guided and unguided torpedoes with anything from no warhead to nukes and they can run slow and silent or scream through the water at over 200 knots.
If you want long distance fire cruise and ballistic missiles work well enough. If you absolutely must have a deck gun it should stow away in the deck under a water tight cover when not it use and fire only at the surface so water in the barrel doesn't over-pressure the barrel. The barrel will also need to have drainage holes that can be remotely plugged for firing in such a way that the plugs won't blow out. The gun should also run the nearly the whole length of either the fore or aft deck of the sub, whichever is longer, to make the violent acceleration survivable to the hardened electronics in the shell. Alternatively it could run the full length of the ship with half poking out the bottom when the gun is elevated. The shells it fires will need a small rocket motor to dramatically extend the range of the shell when burned at apoapsis and internal gyros to fine tune the orientation in flight and especially during the burn so it can actually hit the target. Another way of extending range is to fire submunitions in sabots, a kind of cup or brace that keeps the projectile aligned during firing and then falls away after leaving the barrel. This reduces the mass (making it go faster) and front cross-section (reducing air-resistance) of the projectile at the cost of limiting the diameter of the payload.
I always was better than you, James.