You can use all applicable abilities including both two-weapon fighting and rapid shot. (See this question for a bit more in depth detail about Two-Weapon Fighting.)
More importantly though:
Under Wrist Launchers, we see:
If you are proficient with hand crossbows, you are also proficient with wrist launchers.
This does not mean they act like hand crossbows for how things like Rapid Reload affect them. Instead, it merely means that you're considered proficient with them if you're proficient with hand crossbows. This makes even more sense if you consider the fact that a hand crossbow takes a move action to reload, and a full round action for a Wrist Launcher.
An example of a weapon that copies another weapon is the Aldori Dueling Sword:
An Aldori dueling sword can be used as a martial weapon (in which case it functions as a longsword)
Note that the Aldori Dueling Sword actually functions as a longsword in this case, unlike wrist launchers which merely get proficiency.
Another example is the Dwarven Pelletbow:
A dwarven heavy pelletbow takes the same amount of time and effort to load as a light crossbow (normally a move action)
Unlike the Wrist Launcher, the pelletbow calls out that it uses the same load time as another weapon.
Rapid Reload may not allow you to select it.
Choose a type of crossbow (hand, light, heavy) or a single type of one-handed or two-handed firearm that you are proficient with. You can reload such a weapon quickly.
Note that nowhere in the text of the item is the wrist launcher called out as a type of crossbow, nor is it even in the Crossbows Weapon Group like the pellet bow or tube shooter. The relationship with Hand Crossbows is the only thing linking it with crossbows and allowing it to be selected by the feat.
If we look at the Tube Arrow Shooter, it says:
Reloading a tube is a full-round action, or a standard action if the wielder has the Rapid Reload feat.
Unlike the Wrist Launcher it specifically calls out that rapid reload has an effect on it (and thus implying you can take rapid reload for it).
That aside, I do believe that you can take rapid reload for Wrist Launchers, but this wouldn't net you free action reloads. Instead, using the fact that Tube Arrow Shooter also has a Full-Round action reload that only gets reduced to a standard by Rapid Reload, you would need to spend a standard action to reload your Wrist Launchers.