You most likely will need to make a custom web part to do this. You can wrap all of your 3rd party code int he control and then insert on the page of the checkout process that you need it to occur. I would guess this would be before the user is prompted for the address )you may be able to eliminate this completely). You will need to be sure to use the correct E commerce APIs to enter the data and set it for the record. If you put all of your custom code in your webpart, you should not have to modify the CMS Web Parts.
Check out the Dancing Goat sample site (availalbe during installing) where you can see a checkout process demo. From there, you should be able to decide where you need to add your custom functionality.