No you don't need your university to send these directly. Instead ask your university to put them in a sealed and stamped envelope (stamp over the seal of the letter on the envelope). Then put them in another envelope and mail it to you. Once they arrive, you can put the main envelope inside a new envelope and mail it to WES.
It might be good to also ask your university to give you multiple copies each in a separate envelope just in case the post company messes something up.