Executing JavaScript Inserted Via .innerHTML

What I am trying to do is dynamically update an image and image map on
a page. I'd like the update to happen as quickly as possible and be
done without refreshing the page. The catch is that the image map uses
the wz_tooltip.js (http://www.walterzorn.com/tooltip/tooltip_e.htm)
library to display a JavaScript tooltip containing detailed information
about different areas of the image. So, when I pass the required
<script> tags via .innerHTML, the browser treats it as text and does
not interpret the JavaScript and execute the code.

My code looks something like this: