There are reactor designs - like the 'pebble bed' reactor - that are designed to be inherently safe [zero worries of loss of containment].
I recall [likely 15 years or so ago] a paper study in the USNI Proceedings for an air cooled pebble bed reactor module similar in size to a LM2500 gas turbine module, with similar shaft output.
The LM2500 is the standard gas turbine engine used on US warships since the DD963 Spruance class in the late '70s. It is also used in a CODAG [COmbined Diesel And Gas turbine] electric drive on the QM2 and some other recent ship designs [I think a couple of MSC ships were/are CODAG]
There is much more thermal inertia in the nuke module, so it would not be as responsive to lee helm orders as a gas turbine - likely the nuke would mostly be for base load, and a gas turbine for quick response.