A customer transitioning from S4B to Team is implementing a gradual deployment of Teams where they want to provide the same functionalities of Skype, specifically the ability to share files in a Team's chat (which require users having  a OneDrive license)

They however don't want to enable OneDrive as service per se, outside of the file sharing in Teams chats. They also don't use Teams channels for the moment.

In Teams the Files app/icon can be easily hidden, the OneDrive client is not available on devices, which leave me with the OneDrive URLs to block.

What would be the best way to do this?

Firewalls and proxy are not an option as devices (managed) are used outside the corporate network.

I have looked into Conditional Access and MCAS but they both don't seem to cut it for this use case

There's no way to do that, Teams is built to leverage OneDrive for file sharing, without it this functionality is simply unavailable. You can perhaps add a "tab" with a different storage provider or something similar.

@mikkele The OneDrive service is what runs OneDrive and SharePoint sync so what your users are basically asking for is email with attachments.

Good News !!
yes, it's possible, and you can do that.
need to delete the sharepoint site, unassigned the licenses.
follow the below article to read more.