The problem / issue is, because the function is an AND state, it makes no difference in what order you press the keys. As long as both keys get pressed, the action will occur. So, it is not exactly like a shifted function in terms of safety of accidental action.
Here are some suggestions for what you are trying to do:
P1B8 (Pause) + P2B6 = Exit will give you problems. If you are playing Street Fighter, it will seem weird to guests to say "I want to pause for a minute, don't do a high-punch right now". (Not likely to be a problem if P2 wants to Pause the game because they are unlikely to be pressing Pause at the same instant that they are doing a high-punch themselves). Better option would be P1B8 plus P1B7 to pause, since you are unlikely to use 7 buttons in any game.
However, you still will have problems with your idea - take coin inputs - What you are going to find - P2 wants to insert a coin, presses P1B8 - MAME pauses - then P2B4, coin is inserted, then has to press P1B8 again to unpause. Other way - P2 presses P2B4, (might fire a shot or something unintended, although for coin or start that obviously isn't a problem), then Presses Pause and the coin is inserted, but when releasing Pause, P2B4 is still down, so mame may fire a shot. (This constant pausing/unpausing will drive you and guests nuts).
Two workarounds, but they get away from standard shift functionality but will likely be better for you.
Option 1 - P1B8 is unmapped in MAME, however, you have a button on your panel mapped to P1B8. This serves as the SHIFT BUTTON only. Pressing P1B8 plus P1B4 (set up in MAME) is P1 Start, P1B8 plus P1B5 is Coin1, P1B8 plus P1B6 is Pause, P1B8 plus P2B4 is P2 Start, P1B8 plus P2B5 is Coin2, P1B8 plus P2B6 is Exit Game. The drawback to this is you have to remember a dedicated combo to pause the game (but you could label the CP to make this more clear).
Option 2 - Same as above, but if you want a dedicated pause key, P2B8 is Pause (mapped in MAME) and P1B8 is shift as above, but this requires one additional button on your panel.
Drawback to this method in general are these combos only work in MAME, so if you want to add Nebula or FCE Ultra or any other emulator or game to your cabinet, you are likely out of luck . . .
Other drawback to this - speaking from experience - I play a lot of 2-player shuum'ups (Air Gallet, Zero Blade) for example. In a fast and furious 2-player game, sometimes I lose track that my sprite has died and I need to insert more credits and press start to keep playing. It is much more convenient to have dedicated buttons to reach up and mash than having to remember "Okay need to add a coin, so Shift-P1B5, then P1B4, then release Shift and play), although if that were my only option for all games, I suppose I would get used to it.
Alternate suggestion - I am not a big fan of keyboard or gamepad hacks, but if (in your case) all you need one for is Start, Coin, and Pause and Escape and Select buttons, that would be viable, if you have or know someone with the soldering skills.