Impedance-wise, the shield is just a small bar across the microstrip, SMD shielding cases have usually voids for the signal traces. A shield must have multiple ground plane connections anyway.
All in all, I don't understand which problem you are exactly addressing in your post.
If you have copper pours /ground fills beneath the RF signals traces, they should use via fences. Presuming a continuous ground plane in your 4-layer board, the difference betweeen ground copper pours or void upper layer isn't so important.