Yet another tradition I'm unsure of...rings?

I usually run away from traditional wedding rituals, not because they are traditional, but because I don't totally believe in them. Some things we are cutting out of our wedding are:
- wedding party (everyone is the party!)
- performing the ceremony at the church
- having a traditional religious ceremony
- rehearsals (dinner and ceremony)
- first dance

The one tradition I'm still debating is the exchange rings. A lot of people plant trees, make quilts, or even get tattoos. None of those fit well with our lifestyle, so I'm leaning on a ring to symbolize the celebration of our love. Here are a few that I found on etsy.com.