I'm really sorry but I'm afraid I'm not sure what you were hoping the police would do?
This was an unpleasant incident clearly but not really a matter for the police.
At the very highest point it is a S5 public order and that is being very generous.
It would also need to be in a public place to get over that hurdle.
This is just the type of dispute that happens sometimes sadly in life. It is not really a matter for the police.
I would really strongly suggest that you do not pursue any complaint and do not attend at the meeting. I'm afraid the police will form the view that the willingness to complain says more about you than about the incident. I'm sorry to be so blunt but I know how officers think about the world and they will not think this is good use of scarce resources.
If you are intent then you are free to complain. It is not likely to be decided in your favour though I'm afraid.
They will probably refuse to meet you with a solicitor and, in fairness, it is pointless. It achieves nothing but to antagonise and rack up cost to you.
I'm very sorry but that is the reality.
It is not really correct to say that there was no incident. It would have been more accurate to say that there was not one that required the intervention of the criminal justice system and therefore the police. People have disputes all the time and sometimes they behave badly during them. That doesn't make it a breach of the criminal law.
Can I clarify anything for you?