If the websites are on the same web-server then it would be better to embed the form directly into the relevant pages so that less HTTP requests are required to load the page. To manage the code for the contact form from one central location you could have a common folder on your webserver from which a script (perhaps PHP or ASP etc.) could generate the form you as require, and you could simply include this script or the resulting HTML code into the HTTP response on your contact/enquiry form pages for all the 200 or so websites.
If the websites are on different web-servers then you could follow the same principle but you would need to use an iframe to pull the form into your pages as you suggested.
Ad-server solutions are not an appropriate technology for delivering forms into your pages. These solutions are for displaying adverts onto other people's websites and search engines that when clicked on bring interested people to your website.
Edit on 3rd Nov: Example PHP code snippet for this might look like:
/* If contact form on remote server */
$sContactFormURL = 'http://www.example.com/contact-form.html';
/* If contact form on same server */
$sContactFormURL = '/var/www/www.example.com/contact-form.html';
/* Retrieve HTML and then included it in current page */
$sContactFormHtml = @file_get_contents( $sContactFormURL );
echo( $sContactFormHtml );