Yes, I did that with my old Custom Shop. I found that a pellet tin lid was a snap fit on the sunshade so I left off the BC and just used the lid.
Tin lids being quite cheap, it was worth experimenting and I found that a hole about 10 to 12 mm worked well. Sure, it cut the light but it brought the close ones into good enough focus to see the edges.
Lining the inside of the lid with black insulation tape also helped kill reflections off the shiny surface.