I've spoken a lot about how the Oiler's problems truly lie in not having an empowered bottom six. Unless you're getting a true number one guy, I don't see the point in making a move for a goalie. Stuart Skinner is a good goalie. You can win with a good goalie (see Vegas) and there is no way the Oilers are suddenly going to trade for a bonafide number one out of no where.
The solution is having a bottom six who can compete and who believes in themselves. To do that, having a strong third line center is a must. Enter Ryan O'Reilly.
I don't need to really go into how good O'Reilly is but in a nutshell he's one of the best in the NHL at taking face-offs, plays great defensively, forechecks very well, is a great leader and can put up 50-60 points each year at a 4.5 cap hit for the next two seasons. He would give the Oilers amazing depth at centre with McJesus, Draisaitl and Henrique already there. Also, when they decide to load up the top line, he can play on the second line, and be a very effective second line center. Also he's a proven playoff guy, which the Oilers really need.
With the Oilers in win now mode, I would do whatever I can to make this deal happen.
*edited as I originally indicated he was a right hand shot but was corrected and laughed at by user Adam_emond, lol, thanks!