What movie is this? Cruise ship, deserted island, serial killer, B&W, early 60’s?

Watched this in the early 70’s but never saw it again. Probably not very good since it’s been forgotten but i’ts been driving me crazy. I believe it’s black and white and made in the early 60’s.

Cruise ship, serial killer going around murdering passengers. All we see are deck shoes and khakis. Shipwreck. About a dozen or so end up on a deserted island (no, it’s not Gilligan’s Island). Killing continues. Two of the men (I think) have deck shoes and khakis. One of them is blond and nice and the other is dark-haired and grumpy. Eventually, the grumpy guys gets accused and is shunned to the other side of the island (kinda like Simon in Lord of the Flies). As we whittle the inhabitants down to the last three (an attachtive woman and the two guys on deck shoes), we finally figure out that the blond guy is the killer and the dark-haired guy saves the woman from being his next victim.