No NIP is needed for a mobile phone offence, so the time it takes to serve is irrelevant.
Also if it’s leased it’s very unlikely you are the registered keeper, get out the V5c registration document and check, not that it matters.
After confirming you are the driver you will probably be offered the fixed penalty of 6points and £200, if the matter goes to court the points will still be 6 but the fine will be means tested and you will have the 40% surcharge and prosecution costs on top.
If you needed a witness to help you I doubt you would call them a vigilante?