NO!!! ITS TOTALLY POSSIBLE!!!
You just need your map not to have all the enviromental death types in use (so if your map has no trains or doesn't have deathpits- you're fine!)
Use whatever type of enviromental death that applies to this requirement.
Now, make your death icon. That's the part I have no idea on how to do, but I assume you know how to make your own kill icon,
Make it as a mod to the original death icon (so it replaces it in-game)
Then pack the required texture files into the map. Since this is a replacement to the default icon, it would be displayed instead, but only as long as the map is loaded, of course, since it's packed inside it.
I used this method a lot to make new model skins for my map, so I won't have to mess around with the actual model files. Since you can't mess with kill icons types (they're hard-coded) this is a simple workround.