Not necessarily. It appears that the main use of the secondary and tertiary blades is for shooting them:
So they could be made of aluminum, perhaps with a steel tip for greater penetrating power (although this is perhaps unnecessary given the weak armor of the opponents).
The non-primary swords must also be hollow to contain the rocket propellant. Which I assume is black powder or similar. Should have similar performance to an Estes model rocket, which is pretty bad as rockets go but might be sufficient for a rocket sword. Black powder has a low density compared to even aluminum, improving the mass situation further.
Are you referring to the trident main gauche?
Yep, that looks to be it. Thanks!
Note that the smaller blades are spring-loaded with a button release, so you can keep the blade in a regular sheath.
To be fair, a sword blade that is multiple pieces with a hollow section to insert a tang would probably break the first time it struck anything so it is a pretty dumb idea. But then again, swords are kind of a dumb idea in any world with a powerful repeating missile weapon regardless of how much historical/science fantasy creators try to make them somehow relevant:
Stranger
Or, as seen in the dialog between two NPCs in a superhero game I play, “He who lives by the sword dies to he who lives by the gun”.
I think that is a picture of the sword at the top of this page: https://destroyerbooks.com/
That just looks like a jian with a weird spade-shaped tip. I even own a jian (that I had custom-made for me, they should be a certain length based on your height).
This is a typical jian:
What would a tiny Korean fishing village need it for anyway? Maybe spearing a fish?
Why would that tiny North Korean village be the Sun Source of all martial arts?
Only a pale piece of a pig’s ear would bother to ask such a question!
That’s the biz, sweetheart. 
