Not trading Vatanen for a straight downgrade, not nearly deep enough on defence to do that, we'd be better off just keeping him. We'd need a comparable (top 4) left-handed defenceman in return, so unless we can package Vatanen+ for Klefbom or Nurse I don't see a realistic deal with Edmonton; Sekera & Russell are simply too old and have too many question marks surrounding them.
I know that Edmonton could use some cap relief and cheap talent on the wings to pair with McDavid, Draisaitl & RNH. A trade I proposed on the Devils board was Nurse + Gagner (cap dump) for Vatanen (50% retained) & Wood. We'd certainly be willing to make other pieces (Boqvist, Zacha, picks) available in a trade for Nurse too since he's exactly what we need. Wood is signed to a very team friendly deal for 3 more years (2.75m per) and Vatanen is a very capable top 4 RHD who'd be cheap for this season until he needs to be re-signed for a modest raise at the end of next year, probably somewhere in the range of 5.5-6m if I had to guess. Plus it saves Edmonton almost 1.5m against this years cap to add some more flexibility in UFA.
No idea the Oilers would have any interest in that though, just something that came to mind as potentially being workable when I heard Nurse was potentially available.