It would go something like this:
Put all the skin files on the server:
.u and .int in System
.utx in Textures
In the server's UnrealTournament.ini add the .u and .utx files to ServerPackages= lines listing the package names without the extension. This will make joining players download and be able to see the skin.
If you then want the bot on the server to have that skin you will need to adjust all the appropriate bot sections to assign the skin to the bot in the Server's User.ini file: BotFaces, BotNames, BotClasses, BotSkins etc.
That is an overview of how to do it. I think that is everything, I might have forgotten something there though.