If ethnicity is important to you, just ask when someone contacts you - state that they need to include their name, age, ethnicity etc when contacting you and that you will not respond if this information is not supplied.
In terms of screening, if you are worried someone will try to omit the fact they are arabic or black, ask for government issued ID or their LinkedIn profile. However, be advised that this approach will screen out the vast majority of potential clients as most will not provide these details.
As an aside, weren't you asking about agencies? This is something to consider as you will be required to see clients of all ethnicities...