After going through a list, it seems that most of the gun games in the FBNeo romset use a pump-action reload or do not require reloading at all. Here are the three games that gave me issues with off-screen reloading:
Lethal Enforcers (lethalen): With a controller, I can reload by shooting at the very top or bottom of the screen. With a Sinden lightgun or a regular mouse in lightgun mode, I can only seem to get the reload to work consistently by firing off the top of the screen.
Lord of Gun (lordgun): With a controller, it works perfectly. I can reload off of any side of the screen without issue. With a Sinden lightgun or a regular mouse in lightgun mode, I can only reload by firing off the top or left side of the screen.
Zero Point 2 (zeropnt2): Regardless of using a controller, Sinden lightgun, or regular mouse, I can only occasionally get reload to work by firing multiple times along the edges of the screen. I do not notice a pattern. This game does have a dip-switch to disable reloading and make it play like Zero Point 1, but the FBNeo default has reload on.
A note on the games in which reload only works on some sides of the screen: when the Sinden gun is pointed away from the screen, the cursor will move to the correct border side, but if that movement is exaggerated even a little, the cursor will sometimes jump to another side of the screen. For example, in Lord of Gun, if I move off the left side of the border with my gun, the cursor usually stays on the left part of the border but will occasionally warp to the bottom of the screen and fail to reload. The lightgun system seems to know that the border was touched and does keep the cursor on the border, so there is no danger of firing an on-screen shot. It's like Pointing a Wii Remote away from the screen. The remote and game both know that the cursor is not being pointed at the game area, but neither knows which side of the border to put the cursor on. It would be a non-issue if all sides of the border activated reload when using the gun controller.