No, Indesign's trapping is based on inks, not objects. You can not select an object and modify a trap on a specific object. Keep in mind, to invoke trapping, you would need to print postscript, as opposed to exporting PDF. When printing ps, you can turn on trap for a composite or separated file using "Application Built-In" or "Adobe In-RIP" trap methods.
Here's something you can do in Acrobat (depending on how complex the trap and how many times you would need to alter):
Print composite postscript with trapping on.
Open in Acrobat.
Use the Edit Object Tool and select the overprinted objects that make up a trap, and delete them.
As I recall, my .eps color bars are exempt from trapping while my .ai version does trap.
If the color bar were an image format it would certainly be exempt from trap. (Perhaps a 1200 dpi image.)