AFAIK, this is not possible. It's hard-coded into the game. The one solution I could imagine would be to create an addon that removes the icons used to display the player/other units, but...that's a little extreme
Alternatively, use something like
cadetMode to determine that the player is playing at a lower difficulty level, and add a black screen + message saying something like "THIS MISSION SHOULD REALLY BE PLAYED WITHOUT THE MAP ICONS YOU KNOW". Mind that some people, like Zipper5, prefer to play at a lower difficulty setting that has been modified to be identical to a harder one so that they can access the multiple-saves function (for beta-testing), so this isn't exactly fool-proof either.
Finally, you could simply -remove- the map (removeWeapon "ItemGPS" and "ItemMap" + possibly showMap false), and then add a picture of the area of operations and put it into a dialog of some kind that the player can look at. I think ShackTactical did this at some point. This of course would be a lot of work.
I suggest simply trusting your players to do as you say - I've never used the little icons myself, so I don't really know how much of a problem they are.
Wolfrug out.