Is it safe to moisturize with pure coconut oil?

 I don't see why there would be a problem with you choice of moisturizers. Nevertheless, this is a question that should be specifically addressed to your own surgeon.

I typically advise my patients to wait 6 weeks until they put anything on the incisions because I like the body to first heal the incisions on its own. Once the incisions are fully healed (meaning no areas of scabs), it's usually ok to use creams, lotions, oils, etc. However, every plastic surgeon has their own post op protocol so please check with your operating surgeon prior to applying any lotion or oil on your incisions. 

Check with your surgeon, but generally it's safe to put anything you've used before onto healed scars (don't put anything onto open areas unless specifically directed to).  I recommend to my patients to use micropore tape for 12 weeks following this type of surgery, as it's simple, doesn't need to be changed frequently & helps with the long term appearance of the scars.  All the best

If you have used coconut oil in the past and have no allergy to the oil, it should be safe to use it, once you are healed.  I would avoid placing it on the scabbed areas.  Avoid sunlight on the scars as coconut oil doesn't provide adequate  protection from sunburn.  Check with your surgeon before starting any topical treatments. 

I would keep away from the incision and umbilicus for atleast 4-6 weeks depending on how your incisions are healing. You should be fine applying it everywhere else.