Dead muppet over a Nak metal screen would be only slightly better than a dead muppet by itself. The Nakamichi metal screen is more of a pop-screen to protect the mic from saliva that comes with plosives (t, p, b, etc.) and other sibilants ("s" and other hissing sounds) from vocalists and when used for recording speech. The one advantage to using a dead muppet over the metal screen is the metal screen provides a certain volumn of "dead" air around the capsule that a muppet alone does not provide. If you are starting from scratch, also consider the Rycote softies - very loose open foam around the mic (like a BAS) and a built in fur covering.
note; the above are my opinions based on my experience only and are not based on any scientific testing