My interpretation was essentially as follows.
1. Littlefinger wants Joffrey dead, but he also wants Sansa out of KL and with him. He's a bit of a creeper when it comes to Cat and Cat isn't, well, breathing.
2. Olenna would prefer not to be walking around carrying poison for the sake of appearance of innocence.
3. If Sansa does get caught, she would be completely unable to implicate either of them.
4. Olenna may not have had immediate access to poison and attempting to acquire poison provides an opportunity for whoever you engaged to procure it to talk to the wrong people. So Littlefinger acquired some (or more likely already had it).
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