How to wish happy new year to somebody, that lost somebody dear to them to cancer a couple of days ago?

[i] sorry for your loss I hope the new year brings you comfort and healing blah blah blah[/i] just be honest & sensitive

You do not wish them a happy new year under such circumstances.
Maybe visit and just be there to listen to what they have to say?

That's hard, but write something genuine and from your heart.
I'm sure they will appreciate anything you come up with.

It might be a bit stupid to wish that they are happy. Instead, express the wish that 2021 will hold less tragedy.