If you have an existing setup using Access and VBA, and you just need a better database behind it, could you not just use MySQL without PHP and use the MySQL ODBC driver instead of the Access connection you are using at the moment (assuming you are currently using ODBC to connect to the access database)
This way you wouldn't even have to have mysql running locally if the hit is too high on your local machine and it should be pretty straightforward in that you shouldn't have to make to many changes to your vba code.
Of course, whether this will do it depends on what else is going on in your access db
If not you could try using php and using the PHP Command Line Interface (CLI) which you should be able to call as an external executable from Outlook. Just pass php.exe the name of the php script you want to run
UPDATE:
I am not a VBA expert by any means but it looks like the shell function would let you run the PHP CLI from within VBA
Shell("path/to/php.exe phpscript.php")
http://msdn.microsoft.com/en-us/library/xe736fyk(VS.71).aspx
Of course this will only work if you can get to php.exe on the wamp machine (ie is a local machine or you have network access to the appropriate folder)
Alternatively, if the Wamp server is to be a separate machine then you could trigger the php script to be run by calling a url. I think the XMLHTTP object will do this for you
Dim xmh As Object
Set xmh = CreateObject("MSXML2.XMLHTTP")
xmh.Open "GET", "http://urlofphpserver/script.php", False
xmh.Send