For example, Lor San Tekka could have it, presumably to give to Rey when she is ready
And where would he have gotten it from?
Also Han wasn’t taking Rey to some spaceport, he was taking her to Maz. She is Han’s connection to the Resistance. I don’t remember Han even thinking about any other place to go.
Well where did he get the map fragment? I assume that Luke had given it to him, so it wouldn’t faze me at all if Luke had also given him his old lightsaber. It’s a lot more reasonable than Maz having it.
To your other point: I don’t recall if Maz knew where the Resistance was located. If she knew, why were there agents from both sides among the regulars? It makes me think that Maz had a reputation for being a neutral party. Also, I don’t think Han wanted anything to do with the Resistance before the Hosnian catastrophe. Finn and Rey knew where the Resistance was. They were just there for a ship, they didn’t need Maz’s help.