Never used local bitcoins, so take this with a grain of salt. The way I understand it is, you meet someone in person, give them money for their bitcoins and then they will transfer bitcoin to your wallet right then and there. So unless you give them the source btc address instead of yours, then it has to go to your wallet first.
I would say it would be a pretty dumb idea to have the guy you buy btc from, directly send it to the source. You have NO information about the transfer should there be an issue. Source could say they never got the btc and you have no proof that it was sent.
IMO always a good idea to transfer the btc to a couple of anonymous wallets before you send it out. You could also tumble them ( I don't but a lot of guys do). That said, I have a friend who doesn't even bother transferring to other wallets or tumbling, he has never had an issue, but that doesn't mean he never will.