I don't think it's wrong at all. If your new wife is at least aware of who the ring once belonged to; I think it would personally give the ring a lot more meaning - especially as a family keepsake. A lot of people are encouraging you to pawn the ring - but I think that's extremely unfair to you especially if you have fond, loving memories of your late wiffe and you may regret it one day if you decide to get rid of the rings.
If someone offered me a ring of a deceased spouse, I would take it as a sign that this person is very sentimental and one who deeply values relationships, and simply doesn't disregard the people who were once in their lives and values the times they shared with them, and are willing to do the same with me and welcome me into their lives. And I would be very honored to be a part of that person's life.
You never know, it may even be a sign from your late wife that she in fact wants you to give the ring to your new wife as a sign that she accepts the new woman into your life as your new wife. I think she wants you to be happy; if you believe in that kind of stuff - just how I think personally. But no matter what decision you make, it's not wrong. If a decision does not harm someone else or yourself, then it is not wrong to follow through with.