Web connection through Arduino with WiFi
Effectively what you have discovered (your wireless SD shield) is a method of sending serial data wirelessly, from one Arduino to another, via using xBee shield, wireless shields, etc. What you need to do is to connect to the internet. As you have ruled out ethernet and specified wifi, lets talk wifi shields. 

There are a number of wifi shields available for the Arduino that you can use, though they are generally much more pricey than ethernet shields. 

Here is one from sparkfun,

And another here.

Take a look at the documentation on the http://arduino.cc website for ways to write code for server connection.  

Cheers.