Wrap your shortcode in a div and give it an ID that you can use as a target when triggering your popup. For example, you can put the shortcode somewhere on your page (content, sidebar, etc) as follows:
<div id="popup" class="lightbox">[contact-form-7 id="1735" title="Contact form 1"]</div>
and the link that trigges the popup will look something like
<a href="#popup">Form</a>
You might have to use do_shortcode() in some cases, depending on where and how you add the shortcode.