Yes, but only if you make a ranged attack. For melee attack, the Attack Action can also let you equip it before the attack as well.
If the extra attack of the Light property is a Dagger melee attack as a Bonus Action, then the Free Item Interaction would be needed to draw it before attacking.
Bottom line is that the Hand Crossbow and the Dagger need not be both wielded before taking the Attack Action, as confirmed by Sage Advice Compendium;
So here's the thing- not to add complication to what you're claiming, but look at what the Sage Advice compendium is actually saying- it's not exactly what you are saying.
Can I make an attack with a Light weapon, then draw a second weapon with my other hand and qualify to make the extra attack of the Light property?
Yes. The only requirement for the Light property’s extra attack is that it’s made with a different Light weapon.
The question itself is limited. Technically, all that it is asking is:
If I have a weapon in one hand that is light, and attack with it, can I then draw a second weapon (that is light) with my other hand and attack with it?
That's actually already easy to answer.
Attack action gives you one (ONE!) free equip/unequip. Attack action is attack with light weapon. Free equip of second light weapon in the other hand. That triggers (condition) bonus action. That's all good!
What that doesn't address is a lot of other issues- as I alluded to previously, a lot of confusion comes up in the "free object interaction" (you get to interact with one object that is part of the environment for free).
Now here is where I stand, and I am sure you will disagree.
Utilize [Action]
You normally interact with an object while doing something else, such as when you draw a sword as part of the Attack action. When an object requires an action for its use, you take the Utilize action.
When I read the rules
in pari materia, I don't think that you get the "free" equip of the attack AND a free object interaction. Because:
a. Specific (in the attack action) beats general (something in the environment).
b. Because the free object interaction points you to "utilize," and utilize specifically references drawing a sword as part of the attack action and not the utilize action.
In other words, you don't get "one free equip/unequip as attack, plus one free floating equip/unequip." I think that the rules, together, are that you get a free object interaction that isn't equipping or unequipping your weapons when you do an attack, because that's covered by the
specific rules regarding the attack action.
But don't let me rain on your parade. If and when there is a Sage Advice that really delves into advanced weapon juggling, I'm sure it will be interesting.