Rings and Things

So, I have a ring dilemma. My engagement ring is curved toward the bottom, so a straight ring won't fit up next to it, unless it is curved to fit my engagement ring. If it is curved to fit my engagement ring, it will look funny to wear without my engagement ring. And, I am planning on leaving my engagement ring behind when we go travel around the world. So, I am contemplating buying two rings--one fitted and just a simple band for traveling. My fiance isn't thrilled about this idea. But I really can't think of another solution. Any thoughts?

I wonder if this band would work with my engagement ring, but even if it did, it isn't quite as plain as I wanted for traveling around the world.