Hello.
Although the default Doc Explorer does not allow you filter the class picker, you might try replacing the Doc Explorer with one of the other file listing UI views that does not include the Add button and then use the ECM File Uploader UI View which does allow you to assert a specific doc class to assign the uploaded file.

You can also make a local project copy (or into your own toolkit) copy of the Doc Explorer and customize it yourself.
Also, if you happen to using the latest CP4BA platform, you have access to the new Content Services Toolkit. It requires you have a GraphQL server configured to your CPE (which the CP4BA platform does) and then provides more advanced content related UI Views.
------------------------------
DAVE PERMAN
------------------------------