This is a health and safety issue arising from the workplace and your management need to take it seriously. I honestly find it impossible to imagine that if a staff member of mine was being harassed at work by a client that it would be laughed off.
I also think you need to get your ducks in a row with management before you raise it with him directly. I would suggest a written report / letter covering the following:
X has been making a number of unwanted approaches to you via social media since (date) and outline the number of times.
You have never been anything but professional towards x, and you do not want any outside contact with him. To date you have blocked him on social media and ignored the requests, however he has formed new accounts to make further contact with you.
You have reported it to yyyy in work on (dates) however his attempts at contact are continuing.
This unwanted contact which has arisen as a result of contact in the workplace is causing you stress and anxiety. You find it particularly anxiety provoking when he comes into the premises.
You are planning to speak to x directly to state that you don't want any contact outside of the workplace. You are concerned that by doing so it may result in a backlash against you, either in the form of complaints against you or an escalation outside of the workplace.
You are formally asking your employer for their support and assistance in dealing with this unwanted sexual attention from a customer.
At the end of the day your employer had a duty of care towards you, and they need to ensure this is stopped.