You should understand for what reason your are going to use color attributes. If you want to show this attributes on detailed page - better to have different color attributes and it's allows to manage colors per product kind.
If you are going to show color attributes as filter on category page is also useful for customer to have different kind of color options.
As I correct understand your kind of business I think better one way for you is have universal color attribute (multiply select) and different kind of specific attributes. This will allow customer to see (filter) products by some general color and use additional (specific filters) if you will show it. For example, you can manage filters for each category individually.
Try to group your colors by kind of product without detailed specification:
running_shoe_color
- better to have something like shoe_color
gym_bag_color
- better to have something like bag_color
tshirt_color
- looks good
Create specific color group only if you have a reason to do.
With specific color attributes you can define some exotic color names (for example shades of green), with universal color you need to compare it to some general colors (example green).