J.F.
It would not be awkward. My cousin is Godmother to my 2nd and 4th children.
I wanted to add...are you clear on what a Godparent is? You made no mention of baptism or christening. This is when a Godparent is named. A Godparent is someone who is very familiar with the spiritual beliefs of the parents, and shares in those beliefs and values. The Godparents should be someone whom you trust will instill the same religious values, morals, and beliefs that you will. They are meant to be a spiritual mentor and confidant.