Is it possible to ignore child dependencies in Composer config?

You can ignore packages to be downloaded with the replace property of your composer.json: https://getcomposer.org/doc/04-schema.md#replace

That way you tell composer, that you take or took care of that package’s content on your own.

This can help you to ignore a package your are sure you do not need, but it is kind of hacky. So be aware some things (like tests) might break.
A better approach would be to request a patch from the maintainer of the original package to make the requirements optional (via the suggest property).

edit:
Example for “disabling” the requirement to zendframework/zend-mail:

{
    "name": "my_app",
    "require": {
        "some/package": "0.0.0"
    },
    "replace": {
        "zendframework/zend-mail": "*"
    }
}