Will hairs be removed with the mole or will I require a separate procedure?

Your mole is not difficult to remove surgically. In a few minutes, you could trade it and the hairs for a very fine pink line that would tend to almost disappear over about a year.

An alternative option is to use a laser which works on brown pigment, such as an alexandrite laser. Assuming the hairs are dark, you could get them too. It would however take several treatments, and likely cost more. Also there is no guarantee the mole would completely disappear. 

I would vote for surgical excision by a surgeon experienced in working on the face. 

Most moles do have some hairs growing through the middle of them.  If you excise the mole with stitches then the mole and the hairs should be gone.  If you just have it shaved off, the hairs will remain and can be lasered later if needed and if they are darker in color.  Your dermatologist should be able to explain these options to you and the risks and benefits of both options.