Control who can download my app from the play store

I have an app that I want to be able to distribute to clients from other organisations. I don’t want this app to be publicly visible on the play store, ideally the client would receive a link from me that would allow them to download the app from the play store.

I have had a bit of a search for this, so far I can only find ‘Managed groups’ (https://support.google.com/a/answer/2494992?hl=en) and ‘closed tests’ (https://support.google.com/googleplay/android-developer/answer/3131213?hl=en). A closed test looks to be along the lines of an ideal scenario, however the client would be aware that the app is in a testing phase, and may be able to do more with the app than intended for an end user. The managed groups also seem ideal, but they seem to be limited to my organisation, and when they talk about whitelisting that seems to be more whitelisting the apps on a user’s device rather than whitelisting who can download the app.

Any help would be appreciated 🙂