How to hide the application from the Dock and prevent it from having a menu:
Quit the application
Right-click the application icon and select "Show Package Contents"
Open the Contents folder
Open the Info.plist file in a text editor
Add the following within the <dict> block:
<key>LSUIElement</key>
<true/>
Save the file
To test, restart the application. You'll notice it no longer shows up in the dock nor does it have a menu. You can make the settings you wish and then manually hide the UI by pressing CMD-H on your keyboard.
Don't hide it just yet.
To make it start up hidden when you log in do the following:
Open System Preferences
Select the Accounts pref item
Select the Login Items tab
Drag the application to that tab's list
Turn ON the check-box next to that app in the list
Close System Preferences
Now, in the application, make the settings you want, test that it does what you need (you'll need to turn on the PASS-THROUGH button) and then log out and back in again to test the whole thing.
To quit the application you'll need to use either Activity Monitor or Terminal (kill process#) to quit the process, since you won't be able to get back to its UI to issue a CMD-Q.
If you don't mind it appearing in the dock, then just skip the editing of the plist and at least you'll have the UI hidden at startup.