Engagement ring and wedding band on opposite hands?

I'll be wearing my wedding band on my left hand and engagement ring on my right. My e-ring is a vintage oval halo, and it's an extreme shape with a very low setting, so there is no band that will fit with it without having to slide under and ultimately cause damage to both rings. However, I didn't want to go without a wedding band, so I chose one with some bling, and will wear the rings on opposite hands after the wedding. My e-ring is also beautiful on its own and a second ring just looks distracting with it!

I don't know about wearing them separately, but most of Eastern Europe wears both their rings on their right hand- its because in the Orthodox wedding ceremony, the rings are placed on the right hand, because it it the right hand that Christ blesses with. This is also done by many who are married in the Orthodox churches in the US and elsewhere. My FMIL wears both of her rings on her right hand with an anniversary band on her left hand and FH and I plan to wear our rings on the right, although I currently wear my engagement ring on the left hand.