Would alar base reduction be enough?

Alar base reduction only? No. The entire nose would look to wide if you just narrow the base. Choose a very experienced rhinoplasty surgeon whose noses and reviews you like.

Improving the
nostril width with an alar base reduction is a frequent request of patients wanting
nasal refinement. It is possible to improve the cosmetic appearance of the tip
alone without altering the rest of the nose in some patients. Whether the
optimal option in your particular situation would be a tip rhinoplasty alone or
an artistically performed natural appearing full rhinoplasty would best be
determined at a consultation.
Following the advice from a surgeon on this or any other website who proposes
to tell you exactly what to do based on limited 2 dimensional photos without
examining you, physically feeling the tissue, assessing your desired outcome,
taking a full medical history, and discussing the pros and cons of the
operative procedure would not be in your best interest. I would suggest you
find a plastic surgeon with extensive nasal surgery experience who is certified
by the American Board of Plastic Surgery and ideally a member of the American
Society for Aesthetic Plastic Surgery (ASAPS) or a facial plastic surgeon (otolaryngologist)
that you trust and are comfortable with. You should discuss your concerns with
that surgeon in person.
Robert Singer, MD FACS
La Jolla,California