There is no reason why an entity need take any extra action or interaction in order to make separate attacks with weapons in different hands pursuant to the multiple attacks granted under an Attack action benefitting from Extra Attack. The Rules As Written require neither that attacks come from the same weapon or hand, nor that an attack made with a weapon in either hand is inherently superior or inferior. It is a common mistake to read into the 5e rules the idea of "handedness" or of a main-hand/off-hand dichotomy. However, nowhere in the attack rules is this dichotomy enshrined.
The nature of attacks following from the Extra Attack feature
To follow the chain of rules and restrictions backwards:
... you can attack twice, instead of once, whenever you make the Attack action on your turn.
... With this action, you make one melee or ranged attack. See the "Making an Attack" section for the rules that govern attacks.
The "Making an Attack" section goes on to detail the different types of attacks and their procedures, but it does not reference the selection of a weapon as having any lasting effect other than on determining the type of attack and the relevant modifiers. This is to say, the attacks are entirely separate, not affected by each other in any way. The closest passage to the effect that there is a main-hand/off-hand dichotomy is in the rules for Two-Weapon Fighting.
Why Two-Weapon Fighting does not imply "handedness"
When you take the Attack action and attack with a light melee weapon that you're holding in one hand, you can use a bonus action to attack with a different light melee weapon that you're holding in the other hand. You don't add your ability modifier to the damage of the bonus attack, unless that modifier is negative.
The Two-Weapon Fighting section describes a condition enabling an additional attack using a bonus action, as long as the triggering attack
- occurs during an attack action, and
- is made with a light melee weapon (as melee or thrown),
and the bonus-action attack
- must be made with another light melee weapon held in a different hand than that holding the weapon used in the triggering attack, and
- cannot benefit from the relevant ability modifier.
As written, it makes no note of the impossibility, otherwise, of attacking with weapons in different hands. Rather, it describes the condition enabling the use of the bonus action. Further, the Rules As Written allow for either hand to be the source of the triggering attack, and for both to be the source over multiple turns, undermining the idea of "handedness."
To illustrate, a character wielding a club in one hand and a sickle in the other may take the Attack action and attack with the club, allowing them to then make a bonus action attack with the sickle. For that bonus action attack, the sickle will not benefit from that character's strength modifier, lending credence to the idea of an "off-hand" attack. However, if, in the following turn, they chose to attack first with the sickle, it would then benefit fully from the character's strength modifier, and were they further to take the allowed bonus action attack with the club, the club would then not benefit, despite that the weapons have not changed hands.
Thusly, the Two-Weapon Fighting rules, properly understood, model something closer to "energy distribution" than to "handedness:" an attack made with a light weapon in a single hand leaves some excess for redistribution to the other hand - just enough to use another light weapon, albeit at somewhat less energy than the first attack - regardless of which hand received the initial impetus.
Compare this to Extra Attack, which has no such caveats. Following the same modeling-analogy, Extra Attack simply reflects a greater allotment of energy, similarly distributable to either hand in full or in part.
(Note: even if including feats, part two of the Dual Wielder feat only modifies the conditions for enabling and using the bonus action, mechanically speaking.)
Since there is no part of the rules that requires either that separate attacks following from a single Attack action need be from the same hand or weapon or that there is any difference between hands with regards to attacks, there is no reason why a character holding two weapons which both lack the Two-Handed property could not use each of them to full effect during an Attack action in separate attacks following from the Extra Attack feature.