What part feels wrong?

the 'whom'?

It is normal in colloquial English to use 'who' for object cases (especially if there is no preposition) but more formal language would use 'whom'.

Colloquial:
He doesn't know who to tell.
He doesn't know who to tell about the accident.

Traditionally taught grammar form:
He does not know whom to tell.
He does not know whom to tell about the accident.

You can tell that it should technically be 'whom' because it is the object pronoun, not the subject pronoun.
He tells him about the accident
Who tells whom about the accident?



Or is the problem the lack of contraction?
That will depend on what idea you are trying to emphasise, or what style you are trying to present.

Or is it the structure?
He knows that he should tell someone, but does not know whom to tell.
He knows he has to do something, but he doesn't know what to do.
He knows he has to go somewhere, but he doesn't know where to go.