This is not really a question related to Easy FancyBox but I can help you none the less.
The 'problem' here is that normally in WordPress, shortcodes inside text widgets do not get processed. Only in post/page content. However, there are ways to make WordPress handle shorcodes in (text) widgets.
One of them is to install one of the plugins that are built to activate this function. There are several on WordPress Extend (search for 'shortcode widget' for example)... But I usually use the plugin Widget Logic http://wordpress.org/extend/plugins/widget-logic/ which provides some excellent (but advanced) functions to control the appearance of certain widgets on certain pages/categories/etc. and at the same time it has a neat little option available at the bottom of your normal Widget admin page to activate the so called widget_content filter.
If you do not want to do it via a plugin, you can simply add this line to your themes functions.php
add_filter('widget_text', 'do_shortcode', 11);