I know what you mean but with Fett no longer Jabba's personal bodyguard (taking the Jabba scene out of ANH and having him not bother to attend the Sarlacc party) none of that infamy is on screen (it's just a product of the EU).
So he would seem no more a shady character than any other bounty hunter, sure he could still be famous but on screen he is more of an ambiguous character.