I think you may be blurring the distinction between sense and sensation. It is true that sense can mean feeling, as in
A perception or feeling produced by a stimulus; sensation: a sense of fatigue and hunger
but it can also mean
A capacity to appreciate or understand: a keen sense of humor
So you could use sense or feeling to fill in the following blank:
I had a _________ of having been there before.
But while you might grammatically say
He had a good feeling of humor.
when you mean to say the person had a good sense of humor, it would be awkward and confusing (and would sound foreign to the native speaker's ear) because it would not mean what you intended.
Still, you could easily change the preposition and say:
He had a good feeling for humor.
This version, though related, also has a different meaning.
Definitions from TFD Online