There's a messy way to do this that would fit all your requirements. Of course, a way to do this in game would be better :-P
Backup your character. Really you only need to save one file, <yourname>.URS is the one file that needs to be edited, but if your scared backup your whole character directory.
Place your 160x160 png in the truegfx folder. It will probably help to stick it at the end of whatever series of faces your character is using. In my case I'm a northern guy using north4.png, there are 6 faces already so I made a new one called north7.png
Open up your save game's directory and look for the <yourname>.URS file. A fully featured hex editor is probably the best thing to use here, if not absolutely essential. I tried doing this with programs like wordpad and notepad and every time broke the file.
Find something referring to a png file, in my case it says north4.png. It should be right around offset 535.
Very carefully change the filename to the new one you created and leave everything else alone. Save and see if you can still load your character without the game crashing before celebrating.
Because you added your own new file, none of the other NPCs in the unreal world know about your fancy new face and won't surprise you by wearing it.
filenames: You may be able to name your picture whatever you want but I don't know quite how URW pulls stuff out of the URS file...if you're going to unexpectedly change around a string in your savegame it's probably best to leave it the same length as what as there before.