I would stick with the oak to be consistent. It is OK to have different wood tones in the same area as long as they work together - usually because they are both from the same overall color family - both are brown in your case. What are the floors?

You need to be careful because you are beginning to move in a direction which won't work with the warm wood trim and interior doors - and then it will be a little off with the rest of the home if it is also warmed tone. You are still OK - as both woods are browns, but be careful with other elements. Consider a wall color in the warm green / gray tones like SW Sea Salt or Rainwashed to help bridge the warm tones with the cooler. Cold grays and warm wood tones do not bring out the best in each other, so steer away from cool grays.