"Why" is just a word used as a kind of "filler". It is actually an exclamation as far as I can tell when used that way. It equates to saying; "Oh."
I would advise trying to employ it with any intention. It does not show one to be modest.
It is just a sound. A simple "Thank you." is sufficient.
It serves no useful purpose to adopt an affectation. It looks like a bit of an act, and people quickly tire of acts in public life.
. There are affectations which, when adopted, make one the easy target of imitation and ridicule by others. Similar affectations such as Batting---the---Eyelashes, or moving the hand about in the air with some sort of flair, or turning the head away to show indifference are not tactful gestures in the modern world.