Too many variables... the scenario needs to be more specific.
One thing for sure is you need to deal with this idiot.
Is the buffoon drunk in your opinion? D&D?
Communications are only partly verbal, is he waving his arms around? Is he aggressive?
If he provides his details, you can confirm his address, and with persuasion does he leave or continue to refuse and be abusive? IE does he need to be arrested or can you deal via report or ticket? If you do arrest the necessity is easy - to prevent harm to himself or another....if he continues to tell MOPs to f*** off someone is going to drop him. Prevent commission of further offences, etc. Prevent harm to a vulnerable person (eg the children where harm can be classed as emotional/psychological as well).
s5 would not need to go to CPS, summary offence so charge decision can be made by police. Just make sure you get a brief supporting MG11 from a witness who has had their 'feelings hurt' so the CPS can't dismiss for no evidence offered. With police evidence there is no need to interview for this.
It's pretty simple to be fair and only as hard as you make it. You could simply get the guy to go home once his details are confirmed, then pass the details onto the community harm unit and get him an ASB letter sent out and stuck on the ASB matrix instead. However...............
And it is a big however..............
One glaringly obvious omission so far is that the guy is having a barney with his partner; on the phone or not this is a domestic and needs to be dealt with. If he goes home and assaults his partner, you knew he was having an argument and did nothing, you're going to be having a one conversation with the management, especially if the couple are subject to a risk management plan. Your options are numerous, and would depend on the circs which aren't specific enough by the OP. You could consider BOP for her protection, but if you have a suspicion of a substantive offence like s5 POA then you could lock him up. BOP alone would likely get you turned away from the custody desk. The partner is a witness as she would have heard it on the phone, therefore you've added necessity o arrest by interference with witnesses, and he can be detained in custody whilst you follow up all of the enquiries. Ascertain her details, go and see her, and do a safe and well at the same time. DASH questions and record a domestic. If she discloses that he beats her frequently when he comes home you've got a high risk DV matter to deal with. He can be dealt with as appropriate. Other options are available.
Custody might not like it (if you have custody sgts like ours), but you are duty bound to protect people from harm, and your senior management will support you for taking a positive robust approach.