How to add google reCaptcha to comments when using multisite and several domains

Hi There,
I've been looking around for a solution to this issue. I have a multisite network, and use domain mapping we have around 90 sites with new ones being added daily, each with their own domain name.

I want to add a reCaptcha to my comment forms across my whole network, however, I don't want all my users to have to create their own site keys etc.

I have seen that google allows you to disable domain name validation, however it requires that you "Check the hostname" and links to this article https://developers.google.com/recaptcha/docs/domain_validation

However, unfortunately I don't understand what the article is asking. Do you think you could offer a solution that can be placed in a mu-plugin?

Thanks