Suppose you have a three-armed creature (one of those arms being vestigial) that has Bite plus it has multi-weapon fighting (so it's now holding 3 swords, one in each hand). Can it replace its bite attack with its vestigial arm? It started off with 3 attacks (two swords plus a bite), then got rid of the bite for the vestigial arm (so it's not an extra attack).
A creature that possesses a natural attack typically can't make a different attack if it opts not to employ that natural attack
Choosing to forgo an attack typically means the creature just doesn't make that attack. A creature typically doesn't get something in exchange for opting not to make an attack. (Except, perhaps, the thanks of the creature's foes.)
The alchemist discovery vestigial arm says, "The arm does not give the alchemist any extra attacks or actions per round, though the arm can wield a weapon and make attacks as part of the alchemist’s attack routine (using two-weapon fighting)." Thus, even were an alchemist to possess a bite attack and the feat Multiweapon Fighting, the alchemist can't trade the bite attack he didn't make for an additional different attack or a duplicate attack. He'd've just not made the bite attack, the third weapon attack remaining still an extra attack and impossible due to the discovery. (No creature that I'm aware of has, for example, the option of trading its natural weapon attacks for manufactured weapon attacks or vice versa, but Pathfinder is pretty vast so there's probably an exception somewhere.)
That is, in the same way a typical creature that's wielding a longsword and a short sword can't opt not to attack with its short sword so it can attack attack twice with its longsword, a creature that possesses a bite attack and is armed with three weapons but can only make attacks with two can't opt not to make a bite attack so as to attack with that third weapon.