I forgot to mention other problems, such as issuing dosimetry to the crew and the very real need for routine contamination and radiation surveys to be performed in the public areas - mostly done to have records for the inevitable lawsuits when a passenger develops cancer and says it was because of the cruise ship's reactor leaking. It happens a lot in the commercial nuclear industry - lawsuits not cancers. TVA has it's own lawyers permanently assigned to the nuclear division just to fend off cancer lawsuits.
But wait, there's more! They'd also need an emergency plan in case of a reactor accident, and maintain a supply of KI (potassium iodide) to issue to everyone should there be an accident. This loads up the thyroid so it wouldn't retain the highly radioactive I-131 which would be released.
If people think Carnival got a lot of bad press when the Splendor lost it's diesel power, just imagine the video of a nuclear-powered cruise ship adrift in the Atlantic with a damaged reactor venting radioactive gases out the stack.
Now, despite all of this the Russians do (or did at least recently) have a nuclear-powered icebreaker that accepted passengers for adventure cruises in the Arctic. I'm not sure what type of waivers people need to sign, and I assume the operators are government employees.