Too small a shackle for the load will always be too small and risk breaking.
If you wish to increase the diameter if the pin at the point the lanyard goes around it, a simple slide on sleeve will do it.
The lanyard must always go around the straight pin or you have it backwards to the load.
The webbing is put into an uneven strain if it is installed around the rounded loop, as the ends are more highly stressed than the center.
It is like tearing some thing from the edges first.
Take a sheet of paper and pull straight on it across the entire width, and then pull on it from the edges.
A lanyard anchor that is mounted in such a manner that it cannot follow the direction of pull as the chute moves around, is inviting failure also because the load will vary from side.
Do the same test as before, but this time with a piece of tape to simulate a flat lanyard working against a rigid mounting and a shackle that is allowed to move around.
If using a shackle with a screw in pin that spends most of it's life while not under load, secure it by backing it off from tight just a bit and take a tie wrap through the eye if the screw tab and around the base of the shackle.
Don't use a tool to tighten it.