Is that possible without the need to externally save/export the current

config? In other words, is that possible changing the RCV MAP on the fly

without having to connect to a pc and loading a previously saved MAP?

No, you can only assign one RCV Map. But here is something you can do: 

PC #00 -> 1:1

PC #01 -> 2:1

PC #02 -> 3:1

PC #03 -> 4:1

PC #04 -> 5:1

With footswitches on the TimeFactor, you may be able to easily switch to 10 presets.

Is it possible changing the RCV MAP on the fly without connecting to a PC?

Yes. You can change the MIDI PC RCV Mapping on the unit in the Settings->MIDI->RCV Map menu.