+1 for Nuno's answer. Recognizing that the title of your question is specific to multimedia components, you may want to consider another approach which is to use normal Components, not Multimedia Components. You can create a normal component schema called something like "External Image" that has an External Url field to store your extentionless url.
Content authors will then include these images via regular component linking mechanisms in the Tridion GUI.
You will then need a custom link resolver TBB that will parse the Output item (via Regex) looking for any Tridion anchor tags <a tridion:href="tcm:x-y-z">
and for each one replace them with an <img src=...>
tag where the src path would come from this linked component.
For an example of a similar approach, but with videos, and sample code for a custom link resolver TBB have a look at the code in the following post: http://www.tridiondeveloper.com/integration-sdl-tridion-jw-media-player.