This is what I do professionally, repair technical clothing. I work with many of the major manufacturers on a referrral basis, been in the biz for 10+ years, I work nationally and internationally.

I would NOT take it to an upholstery shop, and I would be sketchy about a regular tailor or alterationist unless you know they are comfortable with the type of fabric and construction. Unfortunately I have seen some real whack job repairs from folks that should not have touched certain garments.

OTOH, it's not rocket science unless you are dealing with taped seams or ultrasonic bonding. It's more of a which hammer/which nail scenario.

If the bottom stop broke off, there's no replacing the part, requires a whole new zipper.

In case you are curious, this is me,
www.specialtyoutdoors.com/about/whatis.asp