Depends on what mod you've got selected in the Skirmisher menu. The default "Nexus Skirmisher" mod uses the ships from Nexus' multiplayer mode and thus doesn't include the Angelwing. However, the Skirmisher also comes with a second mod - "Nexus Skirmisher SP Settings" - which uses the game's ships from the singleplayer mode. There are five Angelwing shiptype variants available: styp_Angelwing15, styp_Angelwing0, styp_AngelwingC, styp_Angelwing and styp_AngelwingM. However, these aren't equipped for battle yet, so you won't have much fun with them (in normal singleplayer, the player would be able to equip the ship during campaign mode, but that isn't available for singleplayer mods).
Better use the "C" button, choose "cls_Angelwing" and create your own ship loadout. Unfortunately that means a lot of trial and error, but there isn't really any better way yet. I've included an example ship configuration, that you can load using the Skirmisher and the "Nexus Skirmisher SP Settings" mod to help you getting started.
