What course of action will I need to take for non-absorbable stitches causing discomfort in my perineum?

Your first course of action is to follow up with your surgeon for an examination. It is very unlikely that a permanent suture was used in your vaginal repair. Often times delayed absorbable sutures are used which take up to 3 months to dissolve - this may be what your husband is feeling.
These sutures may be trimmed (cut shorter) so that they don't cut your husband as they slowly dissolve over time and promote healing.

I think any board-certified gynecologist should be able to remove this stitch. If you can feel it, then this should be feasible in the clinic.

These painful sutures need to be removed. Visit with a board certified plastic surgeon or gynecologist near you. Either physician should be able to help with the problem.