Okay I love coconut milk and the bad news it is HIGH in saturated fat, just like cheese beef and all other wonderful tasty dishes. Well what i have learned is that their are good fats and in MODERATION one can enjoy all things. So the solution stock up on Olive Oil and Avocados which are good in low (good) fats. So get rid of the butter and choose meats which are lean which have less marbling, in other words it should be mostly meat and little fat. But after all the fuss about heart disease etc i say lay off the cheese and choose DAIYA, instead.
While the verdict on coconut milk has many opinions, you can try ALMOND BREEZE which has an almond/ coconut brand which has NO cholesterol. The cholesterol is the problem with saturated meats cheeses etc, they CLOG your ateries, and cause heart attacks and strokes. So you want to stay away from these products.
If you want to be safe you can always try ALMOND MILK or SOY MILK or even PECAN milk as a sub.
DISCLAIMER***** I am not a medical professional so any advice i give is NOT medically researched so you need to consult your doctor before trying any new recipe or suggestion.