http://www.sitepoint.com/article/save-hours-ssis/
http://www.htmlgoodies.com/beyond/webma … hp/3473341
The little bit of html code you need to insert into your pages can be handled in VSD. The question is whether or how the server will handle things. Normally, you would end page names with .shtml instead of .html or .htm when using SSI, but I don't suppose VSD will let you do this. Also, you've indicated that the site is an established one which you've taken over, so it would be best to avoid having to change any page names anyway.
Assuming your server supports SSI, then, as mentioned in the Sitepoint article, you may be able to have your server configured to parse pages even if they end with just .html or .htm.
The basic idea is the sever will parse the pages when they are requested by a browser. If the server finds the SSI include code in the requested page, it will replace that code with the contents of the file that include code points to.
The include code itself looks something like this:
<!--#include virtual="/includes/something.htm"-->
In this example, the include code will be replaced by the content of something.htm, which is located in the folder, includes, located in the root of the site. While this example places the include file in a folder called "includes", that isn't necessary. You can place the file wherever you like as long as the include code in you page points to the correct location.
Since the include code is replaced with the content of the file pointed to, that file doesn't need anything that's already part of the page calling it. Your html page will already have all the header code and the opening and closing body tags, so that stuff can be left out of "something.htm" or whatever you want to call it.
Imagine a complete page of code. You cut a section out of it. Then you put the two together again to make a complete page. Same idea with includes.