Nope, you'll only have to modify code in one place, and you don't even have to leave the Control Panel!

In your Control Panel, follow these steps:
Control Panel> Primary Settings> Style Templates> Your Current Style> Page Down about 3x>
Header Insert.
Then, just pop your style sheet into the box, as you would inside the normal tags. There's no need to add in your own tags, though, because UBB will do this automagically.
Example: