Да

“This hand cream has no perfume and more lanolin because it’s made for a man’s hands.”

Uly, I'm confused. HANDS is plural. Why would we use 'a' article here?

может быть это потому, что артикль относится к man?
[a man]'s hands?

точно!

In this case we could just say ... it’s made for man’s hands. without any article. could we?

Not really. That doesn’t sound as good.

MAN'S HANDS without an article sounds like РУКИ ЧЕЛОВЕЧЕСТВА

I see. Can you give another similar example where we would use A article in a similar case?