[Plugin: Twitter Widget Pro] Alter widget output without modifiying plugin files?

There’s not a ton that you can do to change the output. If you want to use something other than a list you can do that when you register your sidebar that you put the widget it (it respected the various settings there). There are also some filters that you could use to adjust links. Beyond that it has plenty of classnames etc so you should be able to style it however you want without really needing to change it’s output.