My take is that this is a game thing. Basically, in the game you can expect to get jumped by monsters roaming the country-side at any time, out of the blue. So Geralt needs to have 2 swords at the ready.
In the books, if he senses something suspicious out in the country-side, he'll have far more time to prepare and will often know what he is facing in advance. Given his witcher senses, he almost always got the upper hand and isn't likely to get suddenly ambushed, like a careless player of the game could be.
In addition to what's mentioned in TheLethalCarrot's answer, there is also this:
(The Last Wish, Voice of Reason chapter 4)
Geralt speaking to the woman Iola:
As you can see, I carry two. Every witcher does. It's said, spitefully, the silver one is for monsters and the iron for humans. But that's wrong. As there are monsters which can be struck down only with a silver blade, so there are those for whom iron is lethal. And, Iola, not just any iron, it must come from a meteorite.
The game fails to mention this completely and the game mechanics don't reflect this at all either.