You can try using one of the jQuery scrollbar plugins, they allow for customized css design...
You can simply choose to design your scrollbar to be invisible, but mouse functionality will remain...
my personal favorite is malihu's, just make sure to use it's mousewheel extension.
EDIT:
Perhaps after you check out how custom designed scrollbars look, you can rethink showing scrollbars. they are, after all, useful and instructive.
