As far as I know the Azure PowerShell cmdlets do not offer this capability at the moment that I could find. As you point out the Cross Platform Command Line tool does. Since you don't want to add the XPlat-CLI tool to your deployment machines you can use what the XPlat-CLI tool does under the hood: a direct call against the REST api for web site management.
Note you'll need to figure out what webspace the site resides in, etc. You can use the Invoke-WebRequest to make this call so that you can verify you get that 200 response back. Or you could use the Invoke-RESTMethod as well, but that would only return an XML document (the contents of the response). The Invoke-WebRequest provides you a little more control and access to the full response object.
The Microsoft Azure Management Libraries (which the PowerShell cmdlets sit on top of) has a Web Site Management piece to it. One of the operations is an update to a site and that includes a WebSiteUpdateParameters object with a SSLCertificates property. You may check into that as well, though I've not done this myself.