In the poem 'the road not taken' the poet uses a sigh. What type of sigh is it? Is it a nostalgic or confusion or a regretting sigh?

When interpreting a work of art, a person's judgments about the work of art should be based on evidence from the work of art itself.  That still often leaves room for interpretation, but it should stop a person from believing just whatever one wants to believe about a work of art. 

The speaker says in this poem that the roads were basically the same.  There is no question that he did or didn't take the road less traveled--he did not.  The speaker says he did not.  They were the same.

The sigh can maybe be interpreted in different ways, except that the sigh and the last stanza cannot be interpreted as if the speaker is happy because he took the unpopular, less traveled path.  That idea is simply not present in the poem.

I suggest the sigh is similar to a chuckle.  The speaker is preparing to tell a white lie or a big fish type of story.  He is going to play the wise old man and tell a story about how he chose the unpopular path, and say that that has made all the difference.  This is a tale, though.  In actuality, he does not do that.  He may even wish that had been the case, but it wasn't.