Putting it in a VCS undoubtly will give you some headaches as you mentioned. Your best bet is to use Postmans functionality to share collections. Here is from the documentation found at https://www.getpostman.com/docs/sharing
Starting with Postman v0.9.3 you have the ability to share and manage your collections more effectively. The first thing you will have to do is create a Postman account. You can create one using your email ID or a Google account. Once you are signed in after creating an account, the collections you upload on Postman are linked to your account. You can delete them later through the “Shared collections” item in the navigation bar dropdown.