Thinking about it some more, the fact that the sarute is gone suggests the original was most likely silk cord. I think it is unlikely that a metal sarute would simply fall out or fail.
While that is possible, it doesn't explain them all. NCO Type 95's used almost exclusively metal sarute, yet the majority of them in circulation today show up without them. I've never heard anyone say why they go missing. Another possiblity is that when the Allies forced the Japanese to surrender their gunto, many would "deface" them to some degree - rank tassels were removed (maybe removing the sarute in the process?), family crests scratched off, guys turning in rifles often scratched off (or attempted to) the Imperial chrysanthimum stamp. Just an idea.
My dad's Mantetsu still had the stump of the cloth sarute that was originally there, along with a tiny metal wedge that secured it in the barrel screw. So, it was easy to decide which kind to refit it with. If yours doesn't have any pieces inside, then it's really up to you to decide which kind you like. No right or wrong in that.