You can use the reactor in the open ocean where shielding is not a big deal, and switch to conventional fuels when needed.

Nuclear submarines and aircraft carriers already exist in pretty good numbers.

Reactor fuel remains radioactive even when the reactor isn't operating.

And the proposal was a containerised nuclear reactor, so you're going to irradiate the surrounding containers in the process.

Nuclear submarines and aircraft carriers are completely different beasts. The reactor core is very heavily shielded, is built into the ship/boat, and is tended by a team of expert operators, and (at least in the case of US/UK subs) uses bomb-grade uranium as fuel.