That is all completely true in Legends. However, this is technically a story set in the Disney version of canon (because it allows commentary on events in the Clone Wars in a more coherent fashion not because I actually like the Disney canon that much) and the only source that speaks to the matter in Disney canon says the Service Corps don't carry lightsabers. Of course, this is rather contradictory since Dr. Rig Nema is the only known member of the Service Corps in the Disney canon and she carries a lightsaber because her appearance is based on concept art intended for Mace Windu. So, tangled webs and all that. Oh dear, you've given me an excuse to haul out my soapbox on this point. So, in ESB, Yoda tells Luke, in a one-liner for the ages, "Wars not make one great." Despite this, if you look at the body of evidence across all Star Wars material, Luke's original assumption that 'Great Warrior' proxies 'Jedi Master' would appear to be entirely correct. With a tiny number of characters (Cilghal, Tionne Solusar, etc.) excepted, pretty much every Jedi character is a lightsaber-wielding murder machine, and as I've worked on this piece I've come to the opinion that the Jedi Order has it's priorities absolutely backwards. They've taken the Force, this magical power that can do all sorts of things that could benefit the galaxy, and tied up its use in producing devastating combat monsters, and this is doubly wasteful given that if there's one thing the GFFA has in excess supply it's devastating combat monsters (this is one of the reasons that when Nema meets Isoxya the Stoneweb Runner is just kind of lounging around). It's like the entire Order deliberately chose the least efficient use of their powers they possibly could. Consequently, as this work has developed I've tried to highlight that paradox. It's one of the reasons that rather than just making Nema a sort of generic, boringly mediocre lightsaber duelist (there have been several such characters among the Jedi across various works) I deliberately made the choice to have her be abjectly terrible in that regard.