Wow. I would totally get rid of it and get something new for the new person of interest, but that's just me--for exactly the same reasons as you state. I mean... "Yeah, I actually bought it for someone else but it cost me a bit of money (or at least an amount that meant something to me), and I didn't want to lose out on the money (or the points it scores me with a female love interest), so here you go, nothing but the best for you, baby! Oh, and I was thinking about you the entire time I considered re-gifting this piece of exclusively chosen-for... someone else... piece of jewelry..."
Uh, I wouldn't expect the relationship to last long. I would also strongly advise against lying and trying to pass it off as something brand new--ESPECIALLY an engagement ring. God may give her an uneasy feeling about it, and for good reason... and you'd just have to come clean anyway.
Looking at it from the other point of view--I'm sure you gentlemen would NOT want to receive something we ladies bought for another man!!! I haven't been in a relationship in a very long time but when I am, I really like buying things for my guy that I think he would like. But... let's be real. What guy would want to, let's say, receive a sports jersey, along with a greeting such as, "Oh, I knew you'd like it, my ex-boyfriend just LOVED that team and player too and by the way, I originally bought it FOR HIM, but since it didn't work out and you came along... thank goodness it wasn't wasted!! Here you go, O' Love Of My Life!"
Um... I'm thinking... NOT.
Sharp! Good to see you around again, by the way!