You could use browse_rsc() to send the icon to the cache in a way that can be referenced in the browser. Read the reference entry on it, the example should be exactly what you're looking for.

<edit>
It looks like it won't catch overlays or underlays. You'll have to either create a new icon representing the player's "flattened" icon (by blending in their overlays), or by outputting the players icon and all of their overlays to the browser and stacking them (has the bonus of not requiring your players to download a new icon)

<edit2>
I wrote a library for the first method, you can check it out here:
Get Flat Icon

I might write another for the second, but I've got a bunch of other stuff I should be working on...