You can only receive the BT sport tv channels on Youview with a BT TV subscription.
Current pricing and conditions of the BT TV subscription offers mean that for most people taking up the BT supplied box service is the most cost effective way of getting the service on Youview. Your existing box can be used as a second box .
Your (retail) box will still have the retail firmware supplied by the manufacturer (Humax). You will get a different ISP profile because you are changing internet provider - the current Humax (retail) software is compatible with the ISP channels and BT player so were you to take a BT TV package they would function. Note that BT only sells a limited range of packages to retail box owners. The full range is available to those opting for a BT supplied box package.