Yes—this is absolutely an option! As long as you have full-fat coconut milk, then you'll be able to scoop the coconut cream off from the top of the coconut milk and add it to your favorite dishes.
Your cooler situation seems pretty efficient. Not much else to add, besides maybe just pack it with as much ice as possible, and if it's at someone's house, keep it...
Use a ratio of 1 tablespoon (14.77 mL) of water to 3 tablespoons (42.52 grams) of coconut cream for 1 serving of coconut milk. If you'd like to make more...
You can make it with just milk, instead of cream. You will get the best results with whole milk, though some people have success with 2%. Don't use skim.