In your case, you will need to do a few things:
1. Implement your lookup in the CFD using the "session.ani" variable (caller number.)
2. Build the JSON found
here using your result and the CONCATENATE function.
3. Once you got your JSON built, you'll need to use the Attach Call Data, to set the "public_crm_contact" with the JSON content that will provide the information to the Webclient.
Then, simple transfer the call to the queue.
The Webclient should receive that information. I am unsure whether it will get ignored for internal calls tho. You'll have to test that.