Nope, as far as I can tell you cannot have an one button brake in the older games, It'd work if you could multiple bind them to one key but it won't work. Tbh in SBK the Brakes are a whole much different to the ones in MGP13, I can tell you that MGP really has struggling brakes on the front usually meaning checking whether or not your modular should be front or rear but in SBK it is less of a difference as the steels are about equal and I use Back Brake mostly 80% and dossage the Front whereas needed, if at all.
One Thing I noticed when making the Switch that I really had to focus on the Front Tyre Braking, where in SBK it usually was the Corner slinging and getting off Track with the icey off behaviour in the grass or gravel that really was numb and now they came back with rather proper off track physics in MGP. Even when coming from Generations (2012) to SBK08 (2008) I had to completely adjust, braking isn't just quite the problem always it is getting into the proper flow with decent physics, although lacking the extra 20% braking can be tricky at times.