I am going to give an answer, contrary to what I would normally do. That is to say without sources because this will be too long for a comment, yet based on personal experience in handling many different types of sacramentals.
Many priests I know wear the rings of their father when they die, while others have the ring(s) of either of their parents placed into the foot of the chalice they are to receive for ordination (if either one dies prior to his ordination).
As you can see, rings can be easily fixed to the narrowest part of a chalice. Some chalices are able to be taken apart simply by turning the cup and foot in opposite directions. Others are made in one piece.
Not knowing the history of the ring in question, one would have to treat it with respect for what it stands for.
Here are a few suggestions I would like to put forth as in reverently disposing rings or any other blessed sacramentals of the Church.
They can be given (not sold) to someone to be placed on a chalice or melted down to be added to the metal used in a new chalice. I know of some religious who place such objects in the foundations of new churches. If the sacramental (blessing) value has not been comprised, then this is a reverent way of disposing of a nun's wedding bands. Thus it has been returned to the Church.
As long as you treat the nun's wedding ring with respect, there is no sin or blasphemy in possessing the ring, but I would highly recommend that it finds its way "home" in one form or another.