Did you labor prior to your C/S? One thing I hear from mamas is that if they labored, especially if they pushed, after a C/S they have similar levels of swelling/soreness in their vulvas as they (later) experience after a VBAC. So if you labored and/or pushed, things might not be a different as you think.
But that swelling/soreness doesn't take nearly as long to resolve as major abdominal wound healing, generally speaking. IME, within a week or two. The 'standard' six week injunction is not about vulvular issues per se - it's about making sure the cervix is fully closed and the womb fully involuted, which is more important in a hetero relationship where semen is being deposited through penile-vaginal intercourse. If you have a major tear (which is unlikely) vulvular healing could take a long while; but mostly if you have a tear it's going to be a fairly minor one and it will be healed well within that 6 week window (or sooner).
Also just my personal experience - I had a minor tear after my first birth and had about 2 stitches to repair it. I wish I hadn't. The stitches didn't fall out on their own the way they were supposed to and the site of the stitches was very tender and irritated for a looooong time. When I had a very similar tear after my second birth I thought 'well, maybe I'm just supposed to have a little tear there' and let it heal on its own. Recovery time was MUCH faster - and I didn't tear on my third birth (although I think that was more due to position - h&k instead of partial recline like the first two births).