The OP’s case is of a minor accident with only property damage. While it is technically illegal to leave, the cops do not arrest people who left a fender-bender. At worst, it will cause the insurance companies to find him at fault for the accident (even if he wasn’t really at fault.) That is certainly not a reason you can C”V be Mechallel Shabbos for. And even IF it were a case where he could theoretically get arrested for leaving, that is still not a reason you can be Mechallel Shabbos C”V.
What I would suggest is that he leave, and on Motzei Shabbos go to the police precinct to explain and report the incident and why he had to leave for religious Sabbath observance.