I think you can use a piece of software to map mouse keys to keyboard keys.
http://www.autohotkey.com/
JoyToKey can also map mouse keys to keyboard keys
http://electracode.com/4/joy2key/JoyToKey%20English%20Version.htm...but I don't think that answers your question... your question is,
Whats the best way to integrate them:
"Have them as a separate set of buttons - maybe hidden?"
...I don't know where you would hide them, and how convenient would it be to use them when they are hidden?
"Add mouse buttons to existing buttons so they have 2 functions?"
...Now you need some kind of shift-function to engage the mouse buttons, so picture it... you're using the trackball as a mouse, so your right hand is unavailable. Now you need to engage a shift key, like Player1 Start, and reach over and press the shifted left-click button. Do-able, but convenient?
"Not really sure, but I don't want extra buttons on the top of the CP for something that isnt used a gaming button."
...But why wouldn't they be used as gaming buttons?

By default, in MAME, the left mouse button is commonly mapped as an alternate to button 1. Example, the Fire button in Centipede. I like to use my left click button, which is right next to my trackball, instead of reaching up to Player 1 Button 1, when playing trackball games.
And keep in mind, whatever encoder you are using for your trackball most likely has dedicated terminals for Mouse button 1 and 2 already, I know the Optipac does. So if you go with dedicated buttons, you should not need any software solution to get your mapping.
-EVEGames