When a creature takes the Attack Action and attack with a Hand Crossbow, it can now make the extra attack of the Light property with a different Light weapon, as a Bonus Action, or as part of the Attack Action instead if it has Nick Weapon Mastery.
Great answer. Let's be more specific. I'm going to do an analysis on this. As always, the following is my opinion, take it for what you want.
Begin with the action economy- because this will matter. The two actions that matter, for now, are "attack action" (attack), and "bonus action" (bonus).
Absent other modifiers (discussed below) you can draw / stow one (1) weapon (but you can't draw and stow the same weapon) as part of the attack action.
You can either equip or unequip one weapon when you make an attack as part of this action. You do so either before or after the attack. If you equip a weapon before an attack, you don’t need to use it for that attack. Equipping a weapon includes drawing it from a sheath or picking it up. Unequipping a weapon includes sheathing, stowing, or dropping it.
Hand crossbows are ammunition, light, and loading. The key property is ammunition.
You can use a weapon that has the Ammunition property to make a ranged Attack only if you have Ammunition to fire from the weapon. Each time you Attack with the weapon, you expend one piece of Ammunition. Drawing the Ammunition from a Quiver, case, or other container is part of the Attack (you need a free hand to load a one-handed weapon). At the end of the battle, you can recover half your expended Ammunition by taking a minute to Search the battlefield (except bullets/cells).
I would argue that this language (that "draw" is part of the "Attack") tracks the language of the Thrown property- which also allows you to draw as part of the attack. However, there is a difference- an explicit limitation that "you need a free hand to load" in order to draw as part of the attack action that differentiates Ammunition from Thrown.
Why does all of this matter?
Let's look at the Light property.
When you Attack with two Light weapons equipped, you can make an extra Attack as a Bonus Action with the offhand weapon. You cannot add a positive attribute modifier to an offhand attack's damage roll.
And then the Nick property.
The extra attack from a Light weapon can be made as part of the original Attack action instead of as a Bonus Action. You can only make this extra attack once per turn.
To me, without any other issues, I see a problem in pure RAW as the OP stated that there aren't any other feats, etc. going on.
The hand crossbow is limited by the ammo property, requiring you to have a free hand as part of the attack action. So when you attack (using the light property) ....
you don't have two light weapons equipped. You don't get the benefit of the light triggering the nick to cause your bonus action to move to your attack action. And this is specific to the ammunition property requiring the free hand during the attack in order to load (draw) when you attack. While you can equip a light weapon
after the hand crossbow attack, you didn't
"Attack with two Light weapons equipped ..."
Then there's another issue that I see, but others disagree with. I read the "nick" property as stating that the initial attack must be made by the weapon
with the nick property, and the bonus attack (the extract attack) can then be made with a different light weapon that is then moved into the attack action - because it's the attack action with a light weapon
during the attack action that triggers nick, moving the bonus action (with the other light weapon) into the attack action.*
So to answer the question- in my opinion, if you ignore further complications (feats), the interplay of weapon properties and the action economy means that using hand crossbows is usually not a great idea.
I will caveat all of this somewhat-
1. The thrown property (which means that a thrown dagger, for example, can be considered "equipped" even when you don't start the attack with it in your hand) would allow you to start the round with the light crossbow, throw a dagger (nick), and shoot the crossbow (since you have a free hand and its light) as an attack. Not sure why you'd want to, but you can.
2. I think the restrictions on weapon juggling and the action economy are neither here, nor there. They prevent the worst abuses if they are followed, but they also don't make a lot of sense in general. I happen to think it's a good idea to follow them, but if your group is into weapon juggling and powergaming, do the things that seems most fun for your group. Personally, if someone had a cool idea for a character that was going "pew pew pew" with two handcrossbows, I'd work with them to make it work and make it fun.
*Weapon properties, cleave, nick, etc., are invoked during the attack action with that weapon. It has to to be used in the attack, which then moves the bonus light weapon attack into the main attack. This usually doesn't make a difference, except the few situations when it does. But it's not the
bonus attack that has to be nick- it's the attack.