Your original proposal was unnecessarily involved - the output from the FTDI adapter is the 5V directly from the USB connector and as best I can see, it is un-fused. (How do I know? Well, the Polyfuse would have to be the same size as the one in the Uno and there simply is not enough space on the FTDI adapter.)
You just take power from the same connection that feeds the Pro Mini. If you need overload protection (and once the system is fully developed and built, you have to ask: why would you need such protection?), you use a Polyfuse device for exactly the same reason it is used in the Uno - because it performs the task correctly and simply.
Resettable fuses of this sort are indeed slow. They are thermal devices. That is so that they do not actuate on overloads which are too short to do any damage. The USB port from which this is all operated has current limiting (though this may not be so evident if you use a power supply instead of a computer) and will not be damaged by overloads long enough to actuate the Polyfuse.