The scrollbar is a browser feature. If you want to use a custom control for this you are free to do so. If it needs client-side initialization I can suggest using the OnClientResponseEnd event
as the first time the content of the tooltip is available, the getCurrent() static method shown in this article
to get the shown tooltip and the get_contentElement() method from its client-side API
Of course, if you have a server control that will do this for you, you can add it in the user control loaded in the tooltip manager.
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