Flambeau Outdoors 4007PK3 Fishing Tackle Boxes - 3 Pack, Includes 36 Dividers, Clear Tackle Box Fishing Lure Organizer, Tuff Tainer Tackle Box with Zerust Anti-Rust Dividers

Maybe you can get some kind of tackle box organizers like this one that you can put your pieces into as you cut them out and close when the cats are nearby or in between building sessions? I use stuff like this to keep pieces separated by body part while I’m painting or panel lining so that I don’t have to worry about finding those tiny parts or figuring out whether they go to the left or right side of the kit.