Stropping Wilkinson blades

[str8six]

There's evidence the stropping handle from this old Wilkinson Dunhill set has seen plenty of use--wear, remnants of stropping paste, etc. But it's a very loose fit, doesn't hold the blade tightly at all, it just falls in (and back out). Before I crimp it with a pair of pliers ...am I missing something? Maybe I'm supposed to wrap something around the spine to protect the blade?

https://imgur.com/a/Fy2VNwP