Sure. We’ve had nuclear powered merchant ships in several countries: Japan (Matsu), USA (NS Savannah), and ten civilian nuclear-powered vessels have been built in theand . Nine of these are icebreakers, and one is a container ship with an icebreaking bow. All six nuclear-powered icebreakers of the Arktika class have been built at the in . Vaigach and Taimyr were built at the in and then brought to Russia for installation of the and .
So, you have your yacht built in Finland, get a Russian reactor, and flag your yacht in some third world country where you can grease the palm of the necessary officials to get a “flag of convenience”. Congratulations, you now have a big nuclear powered yacht.
Good luck being allowed to pull it into port ANYWHERE. See the experience of Matsu. you can sail or rent it in some countries Like United Arab Emirates (Luxury Yacht Rental Dubai)
Nuclear powered ships have been built.. But operating a nuke is not simple or easy and the backup you would need is probably beyond even a Russian oligarch.
However, if you have enough money you can charter a Russian nuclear icebreaker. You just can’t travel to or past the equator because the water is too warm for the ship’s cooling system.
Actually… you could go into the Russian icebreaker business, and operate out of Russia, and just modify your icebreaker have a few super luxurious “owner’s suites” onboard, and skeet shooting off the stern, maybe a small submarine, speedboats,and other accoutrements of luxury yachting. Still not sure that they are going to welcome you in the Mediterranean if you want to catch the Grand Prix in Monte Carlo, or the Cannes Film Festival…..