You didn't realize this is wrong ?
If you make a server only mod, it isn't supposed to have a client part at all.
Doesn't make sense to me. Your "Server Mod Only" actually works like a Universal mod, and thus you don't need a "Client Mod Only", since you can merge it in the first one.
If "put on client mod" means installing it, you can't do that. It isn't possible to download and install a mod without restarting the game.