Is it possible to hide a custom field type plugin from the popup tab when double clicking an entry?
If you're looking for a setting you can apply to the plugin that corresponds to your custom field, it doesn't look like such a setting exists.

Update: I was just made aware of this Craft CP JS plugin in another question. It looks like you could potentially hide your plugin from displaying. It's not as elegant as a first-party solution but it may be worth a shot