This is something we've had issues with as well - perhaps this solution may help you.
The general idea is that you have a group of elements with arrows at the top and bottom (these can be clicked to scroll). The user can also use a scroll wheel inside the area to scroll. There's no real affordance of scrolling here, but it provides an alternative method for your users to navigate (and further, allows its use on touchscreens if that's a future application).
download bmml source – Wireframes created with Balsamiq Mockups
The affordances for scrolling/further content are twofold - firstly, the arrows appearing denote that there may be more content. The second is the fading at the edges, which acts to counteract the tendency for solid objects to act as the edge of the list's gestalt (this is the same principle as people not realising you can scroll below the page fold of a page where all the elements end just before the fold).
One other option is to go with the OSX idea of appearing scrollbars as @JonW mentions above. The issue there is still with affordances for scrolling, but one method of fixing that is to cause the scrollbar to appear onHover, rather than just when the user is trying to scroll.