Is it necessary to wear your engagement ring with your wedding band?

The matching wedding band to my ring is over $400, and I found bands I love way more than that one for under $200. The only problem is those bands won't line up with my engagement ring, so I would not be able to have them welded together after the wedding and there would be a very noticeable gap all the time, and my engagement ring is a Solitaire and snags on things occasionally anyway. The diamond is an heirloom from my fiance's great grandfather passed down in the family and I really want to keep wearing it. It's beautiful. Just don't want to spend a lot on our wedding bands. I guess I could wear both on our wedding day, but after that, I'd probably never wear my engagement ring anymore.