This would be the only solution if you are using Ableton to play live.
I don't use Ableton, so don't know if you could tune individual notes in a sample library, in the way you can in Kontakt, for instance. (If all notes were equally out of tune, this would suggest some kind of global problem, such as erroneous pitch-bend messages, or some kind of global fine-tune setting being off.) This is also suggested by your comment that some other notes are out of tune, but by different amounts. From the comments provided by it sounds like you don't have a problem with your setup, but that the strings library you are using has some out of tune notes.