The tsunami is radioactive only if the detonation occurs close to shore. A longer stretch of coastline can be swamp by detonating further from shore, but its radioactivity remains around the detonation site. The tsunami wave FORM travels outward from the site until it reaches the shore and becomes a tsunami.
Radioactive on not, its is an indiscriminate weapon and thus illegal. The same holds for nukes generally: they are barbaric weapons and no civilized military leader should have or want them in their arsenal. The G20 said clearly enough: "The use or threat of use of nuclear weapons is inadmissible." (Bali, November 2022)