All the images drawn from the Skype website do not have transparent backgrounds, so unless your website has a white background, then the status image looks a bit out of place.
After a little research, I discovered that you can make a call to the Skype status page for your username, and receive a status back which you can then use to display any message or image you choose.
Check the Resources at the end of this tutorial for details.
Originally, as I am a complete noob to building modules rather than just customising them, I tried to use the fopen() system of getting information from external websites, but eventually I learned that using cURL is the way to go.
To use the module, you must have cURL installed on your host - check using this tutorial.
So I built a module to overcome this problem.
Instructions:
(1) Download mod_transparentcustomskypestatusbuttons from the Downloads section of this website

Version 1.0.1 is now available that checks to see if you have cURL installed and displays an error message if it is absent :)
(2) On the Administrator page go to Extensions - Install/Uninstall

(3) Upload the Zip file you downloaded earlier.

(4) Once you receive the 'Installation Success' message - Go to Extensions - Module Manager.

(5) Choose mod_transparentcustomskypestatusbuttons from the dropdown.

(6) Click the link to start editing.

(7) On the Details section, decide if you want to change the Title, whether you want to display the Title, and which module position you want the module to display in.

(8) Pick your Menu Assignment or Assignments - I only want my Skype Status on my Contacts page for the time being.

(9) Now the fun bit - you can set a few parameters for the module.
You can choose to have the module aligned to the left, the centre (I'm British so it's centre, not center) or the right. I've also allowed for some text before your image is displayed and after it is displayed.
You can choose between 3 types of image (I've altered the Skype Images to be transparent).
The Speech Bubble type

The Boxy Type

A Customised Version (I've included a set of customised images, but you can change these yourself - instructions for this are later in this tutorial).

I apologise for the very basic formatting, but it's adequate for my needs, if you want it slightly customised, let me know, or make a suggestion for the next version and I'll do my best :)

Don't forget to put your Skype Username in rather than leave mine there!
******Very Important Message Follows ******
For this (or any Skype Status) system to work, you have to adjust the settings on your Skype to allow the Skype servers to know when you are online etc ...
Ok - First of all boot up your Skype ... Click on Tools then Options

Now click on the Privacy Button

Now you need to clcik on the tickbox that has the line 'Allow my online status to be shown on the web' - if you don't do this, you cannot show your online status to those on your website.

Now click Save and you are ready to continue to use the Skype Status Module :)

(10) Once you have made all the changes to the parameters that you want to, you need to Save your changes :)

(11) Now navigate to the page you set the module to appear on ...

Try changing your Skype status and refreshing the page to make sure everything is working fine!
(12) If you want to create your own transparent png's to show your status, you need to follow a few simple instructions.
(a) Create a set of images that are named as follows - unknown.png, offline.png, online.png, away.png, not_available.png, do_not_disturb.png, skype_me.png

There is actually a code returned for 'Invisible' but for obvious reasons, I get this to display as 'Offline'.
(b) Now open up your favourite FTP program (or use cPanel if you prefer) and navigate to the folder modules/mod_transparentcustomskypestatusbuttons/custom/ this is where the custom images are stored.

Upload your replacement images
(c) Now edit the module in the Admin section to choose Your Customised Images

Check the result -

I'll upload the Photoshop files of the customised Skype Icons as soon as I can, as well as the references for where I got all the clever stuff to build the module.
PSD Files are now available in the Downloads section :)
Resources:
Building a custom Skype-me button with status icon - an article from the personal blog of Nicolò Volpato that helped put me on the right track :)
Smarty skype status function plugin - a plugin for the Smarty (Template Engine) that helped with the cURL setup.
Skype Status Class - A PHP class from the brilliant http://www.phpclasses.org/ - this class written by lubosdz. I was originally planning on building a module that checked the status of several Skype users at the same time (to be used at my workplace for an online support system) - I played around with the idea for a while and used this class to run a few test ideas, but bottled out and made the simpler version first :)
Have fun with my module :)

There were quite a number of excellent modules available and I quickly installed one and had it up and running ... unfortunately it looks a bit untidy on my website with its contrasting background colour :(