Wearing a ring on both hands?

I am getting married next month and recently picked up the wedding band I will be wearing.

For the past 3 years I have been wearing a fraternal ring on my right hand. It’s a stainless steel ring which I always wear, and feel it works for both formal and casual situations. I wear it more for the meaning, than the style.

Now that I will be wearing my wedding band on my left hand forever, would it be over-the-top to continue wearing my fraternal ring on my right hand? Both mean a lot to me, but obviously my wedding ring carries greater importance to me, if I had to choose.

Should I retire my fraternal ring?