You could try a free open-source javascript script called 'swfObject.js', which is a cross-platform, cross-browser compatible javascript file which can detect the type of browser being used and attempts to detect the version of flashplayer installed before generating appropriate, browser specific HTML to embed the .swf at runtime.
If no flashplayer is present, you can simply specify alternate content to use.
Check out the swfobject project page here:
http://code.google.com/p/swfobject/
With swfobject.js, you can: specify the .swf file to embed in the page
specify alternative content if no flashplayer is installed (i.e. the image you want to display!)
specify the minimum version of flashplayer required
pass flashvars, params, attributes to the target .swf.
It's a pretty robust script, it's used widely and it's got quite a large community of users and contributors/maintainers, so if you do get stuck you can always post a question on their forums.
There is also a downloadable tool which will help you to create the appropriate HTML/javascript code for your page (available as a dynamic HTML page or an Adobe AIR application). You just fill in the path/name of the swf to embed, set any of the other myriad of options and then click the 'generate' button to create some code which you can cut/paste into your HTML page.
If you download the latest version of the script and put a copy of it into the js folder of your website, then download and try the configuration tool to generate the appropriate code for your HTML page. You should be able to generate the code required for your web page in a couple of minutes.
It really is that simple!
Cheers for now,
Jas.