For clarification, do you mean to hold the first slot's cavalry firing(Hold Left-click) while activating Dual-wield, OR just take your first cavalry out in your hand and activate the skill?
In semi-auto mode, you should repeatedly press fire button to shoot. Were you holding right-click when trying to shoot? Or the weapon was not working even if you spammed right-click. And if you use sniper rifle, is zooming working(right-click button working)?