The "e" columns being open is not an issue for king safety. Your king is only there temporarely. After ...exd5, Black would probably follow with ...Bd6 and ...0-0, then at some point ...Re8 to exploit the semi-open file.
...cxd5 is a playable alternative, but your c8 bishop would become a much worse piece. It's hard to see how you'll liberate him with an ...e5 breakthrough, so he'll stay "trapped" behind your pawn chain for a long time. White could also have the opportunity to play quickly on the queenside with Bd2 and Rc1.
Finally, after ...Nxd5 we are probably leaving too much space for our oppoennt on the center (we're allowing an e4 push)