To get back to the original question; a shooter.
My opinion: Don't use a matching numbers Luger as a shooter regardless of the maker being DWM or Mauser.
Find a non matching numbers Luger in good condition and use that as a shooter. It's more economical and you won't "destroy" a good collector's item

BTW Mauser Lugers are just as collectible in my opinion. Especially the last ones from 1942.