You are always playing a mod when using the Skirmisher. Per default it uses the "NEXUS Skirmisher" mod, which contains all the ships and the weapons from the main game's multiplayer mode.
If you're just looking for the "real" names of the weapons, then open this file:
modsuniversetextstextsdev_weapons.ini
If you're using the default "NEXUS Skirmisher" mod, replace with "NEXUS Skirmisher". The file contains the in-game names and descriptions of each weapon. After opening that file search for the weapon name being displayed in the Skirmisher. For example: on your screenshot there is a "weap_gun" - when searching for "weap_gun" in the file, you'll eventually find this text:
"gatling gun"
"High fire-rate plasma weapon against hulls. It has relatively small energy. It does not pierce through energy shields."
You'll probably also see translations of these names and descriptions, e.g. in German:
"Gatling Gun"
"Plasmawaffe mit hoher Schussrate gegen Hüllen. Sie besitzt nur relativ wenig Energie und durchdringt keine Energieschilde."