Welcome to the forums!
I'd recommend starting by testing your electronics before putting them in the cabinet. Connect the guns to the A-Pac, connect that to a PC, and see if you can get MAME to properly read the pots in the gun. You may need to edit settings in MAME to get it to work properly. Don't worry about getting the guns perfectly calibrated or the buttons mapped correctly. Just make sure they're being seen by MAME at this point.
If you're more likely to use the Pi for this, I'd still test the stuff on a PC first, then get it working with the Pi.
I'm guessing you plan to use the other parts in the Operation Wolf cabinet? If your cabinet has all the original artwork, I'd suggest making a new control panel top, and trying to sell the old one with the artwork and the instructions. Best not to ruin good artwork when you drill holes and mount the guns.
How you mount the monitor and other stuff (like a sound system) depend on the cab design. When in doubt, take some pics of the inside of the cab and the LCD, and ask for advice.
Another thing to consider is how to select the game to play from the front-end, since you won't have a joystick. Maybe the left gun's trigger goes to the previous game, right gun trigger for next game, and player 1 start button to start the game? Just a thought.
Your Operation Wolf cabinet should have a coin door. Looking at the original manual, that game didn't use a test button (it used dip switches.) I'd recommend adding a test button (mapped to F2) somewhere inside the coin door, so you can get to the in-game setup of some games (like Terminator 2 or Revolution X.) Also put a quit key (mapped to ESC) inside the coin door to quit back to your front end.
Don't forget to take lots of pictures and post them here. You can upload them to a sticky topic above ("NOT A PROJECT IV - Thread for Posting Images to Link in our project threads"), then post the link to that image in the actual build post. Makes for a clean looking post, and the pictures won't disappear when some random image hosting service goes down (which has happened to some older builds.)