Can I apply a thin layer of coconut oil or other natural oil after on my eyelids after blepharoplasty?

I had upper/lower blepharoplasty 7 days ago, and my sutures were removed at day 6. The suture lines feel tight, particularly when I laugh or smile. Is it too early to begin using a natural oil (like coconut oil or rose hips oil) on my suture lines? My surgeon said to not use Neosporin as this could irritate the suture lines. I've applied a very thin layer of coconut oil to deep cuts to reduce scarring (with fantastic results), but I wasn't sure if this would be appropriate for incision scars.