Your small wire may go to your trailer's control panel.
I am not familiar with the converter you are replacing, but the old OEM Univolt in our 1973 Sovereign
had such a wire, which ran to the control panel where it lit up the 'shore power on' light.
To help identify the function of your mystery wire, check the voltage on it when the converter is plugged into shore power. If you see the DC output voltage on this wire, a good bet is that this wire went to your monitor or control center.
When I replaced the Univolt there was no connection for the 'power on' light on the new converter. I missed that little night light up there--a 'status ok' assurance when things got dark.