Advice With Collision

Hey all,

I am struggling with finding a way for objects to collide smoothly. I have a pool cue, and I want it to be able to rest on/inside an object while the player is lining up their shot similar to a granny stick. The two objects both have convex object colliders and both collide with each other, but the pool cue won't fit inside the mouth of the granny stick. I can see that the convex mesh collider is going over the spot where I want the pool cue to go inside, so my question is how do I make a more specific mesh collider such that the mesh covers only the parts of the object that I want? Essentially, I want to control what parts of my object have collision by adjusting the mesh.

Any advice?