Since learning about it a few months ago, I did a bit of checking. The metal was always there anyway, being the structure of the weapon, with the 'sleeve' just slid over the top. I used to have unlimited access to an armoury literally full of weapons from ww1 to present, including a MG15 for ground use, with a water cooled barrel jacket, which had a steel butt, so no sleeve, and another, from (we think) a Ju88, which was date stamped as 1943 on the original inspection tag still attached to the weapon. This was hanging on a wall, and i hadn't realised it also had the wooden sleeve, as the timber had darkened to virtually black.
I've looked at quite a few B&W pics over the last couple of months and, although it's not possible to be absolutely certain, it seems that all of the aircraft-mounted weapons had the sleeve which, as I mentioned, was a protective measure to prevent scorching of the gunner's hands . I've even tried to ascertain if the weapons mounted on the CASA 'Heinkels' in the BoB movie have the sleeve, bearing in mind these were post-war, but haven't determined that yet!
I think it's a fairly safe bet that where a Bf110 mounted a MG15, it would have the sleeve. When the MG81 zwilling was mounted, for example on the Bf110G, then that was 'controlled' by the single, central pistol grip/trigger, and a 'butt cap', with rectangular receivers, and therefore no sleeve, or requirement for one.