To solder or not to solder?

Hey ladies! I just married my best friend about a month ago and I'm wondering if I should solder my engagement ring and wedding band together. I only ask because they don't exactly match (as you can see in the picture) and the band is so beautiful, I thought I might wear it by itself sometimes (but honestly probably not). Anyways, give me your opinions/experience or other ideas to keep the rings together so they don't rub each other! Thanks and much love!