Yes, you can
The Two-Weapon Feint feat has only two requirements:
1) "While using Two-Weapon Fighting to make melee attacks". If you are using your melee weapon to make melee attacks, then this requirement is met;
2) "you can forgo your first primary-hand melee attack", which can be done if your primary hand is wielding a melee weapon.
So, when making a Full Attack with a sword and pistol, for example, you could spend the first sword attack to make a Feint maneuver against an opponent within your melee reach. Then make an attack with your pistol, as described under Sword and Pistol, and then proceed from there normally.
You simply couldn't do this if your primary hand was wielding a ranged weapon, or if both of your weapons are ranged weapons.
There are ways to Feint with ranged weapons
The Ranged Feint feat (Ultimate Intrigue) allows you to use the Feint maneuver with ranged weapons, using the same action used to feint:
Benefit(s): You can feint with a ranged weapon by throwing a thrown weapon or firing one arrow, bolt, bullet, or other piece of ammunition; this feint takes the same action as normal to feint, but depending on your weapon, you might have to reload or draw another weapon afterward. When you successfully use a ranged feint, you deny that enemy its Dexterity bonus to AC against your ranged attacks as well as your melee attacks for the same duration as normal. If your feints normally deny a foe its Dexterity bonus to AC against attacks other than your own, this applies only against others’ melee attacks.
Normal: You can feint only with a melee weapon, and only against a creature you threaten with that weapon.
Similarly, the Feint from Shadows rogue talent (Blood of Shadows player companion) allows the same, but you must be concealed and within 30 feet of your target.
Which, in most situations, means using a Standard action. But if you figure out ways to feint using an attack that doesn't say specifically that it must be with a melee weapon (ie: not Two-Weapon Feint), then you could also make ranged feints during your attack sequence.
I can only think of one feat that could do something like this, Out of the Sun, but it is a teamwork feat and the benefits are applied to your ally. However, that doesn't mean that there aren't other ways to achieve it.