- For Olenna, the frills on the plan make it more palatable: she gains a scapegoat with few living allies who everyone powerful will want to blame, she takes fewer personal risks stashing poisons etc, and she doesn't have to skulk around treating with common poison-peddlers. But she still gets to do the deed (rather than trust some oaf to not botch it). It's perfect for her.
- For Littlefinger, the frills on the plan may make Olenna's plan more complicated with more possible failure points: but each way it could fail still suits his interests, creating useful, usable chaos. Don't think of it as a dastardly plan where he has his fingers crossed hoping all the pieces fall into place, that's not his style. Think of it as artfully creating a situation where almost every possible outcome strengthens his position and weakens his enemies.
For Olenna: the benefits of the scapegoat and less time hiding poisons are obvious; but
also keep in mind her personality. She doesn't even bother learning the names of her bodyguards: can you imagine her sneaking into some common criminal's tavern to secretly fraternise with some foul-smelling, unkempt and probably unspeakably unreliable poison smuggler? Sounds wretched.
Or even worse, she'd have to receive the poison from Baelish before he set sail, then keep it hidden for a long stretch of time, probably in her own personal quarters, in a city she can't stand which she considers (accurately) to be ridden with spies. While she doesn't mind offending people, she's very risk averse when it comes to actual personal risks (for example, she goes everywhere with two bodyguards, she takes precautions to ensure secret conversations aren't overheard even when there's no-one around, etc).
Exchanging letters with an intelligent and efficient minor lord, then plucking poison from the hair of a pleasant, safely silly, well-groomed young lady sounds much more palatable.
For Littlefinger: I think the other answers and the question are based on a subtle but very important misunderstanding about his schemes.
He doesn't do complex delicate plots that depend on good fortune and X, Y and Z all falling into place exactly as intended. Varys does, and these seem to go the way "the best laid plans" go in real life: nothing ever goes exactly according to plan. We see the pawns in Varys' plans getting so fed up of him changing the details every time circumstances change, they decide to do things their own way, forcing Varys to change other details, kill people he hadn't wanted to... What did Littlefinger tell Sansa about even the smallest pawns having minds of their own?
Don't think of Littlefinger as a cartoonish supervillian with cartoonishly elaborate plans which, in real life or well written fiction, collapse like a house of cards the moment one piece slips slightly out of place. Instead consider his apparent mantra: chaos is a ladder.
His schemes embrace uncertainty and probability, setting up situations where whatever happens, he's strengthened and his enemies are weakened.
In this case, consider the possible outcomes:
Olenna is caught or observed administering poison. Lannisters turn on Tyrells, possibly bankrupting themselves or at least creating hunger and chaos. Both the most powerful houses are substantially weakened. With Littlefinger's distance and lack of motive, any attempt by Olenna to implicate him will look desperate and has no reason to be believed. Sansa is either:
- Bundled into a boat, fueling Cersei's paranoia, implicating Tyrion, adding the possibility of a Lannister implosion at the same time as they lose their most important ally, and gaining Littlefinger a useful pawn
- Caught, with Ser Dontos. Olenna, Sansa and Tyrion all go on trial at once, and their stories are bafflingly contradictory. Much chaos and confusion, much paranoia fuel, and plenty of opportunities to turn people against each other.
Assassination succeeds. Sansa is discovered missing. Tyrion's arrest is later and is less dramatic (no-one could have predicted Tyrion implicating himself so badly), and the case against him is less overwhelming - meaning even more internal Lannister division and discord - but otherwise things pan out exactly as they did: much paranoia, much chaos, House Lannister weakened, and much leverage gained over the matriach of one of the most powerful houses.
Sansa is somehow caught with the poison, before Olenna can take it. Her and Tyrion are immediately under suspicion of planning treachery. The (still living) Joffrey goes berserk, House Lannister turns on itself. Chaos created, enemy weakened, minimal risk (Olenna will keep quiet, Littlefinger is miles away and seen by Joffrey as an ally). Littlefinger has information (the Dontos connection - who has no reason to be told who was behind his being hired) which he could use to sow paranoia or gain favour, depending on how things go. He also has a devastating secret about Olenna which might be useful blackmail fuel...
...And so on. Almost every possible or probable outcome created chaos and paranoia Littlefinger can use, and discord and distrust he can exploit, and weakness which will be useful if and when he wrangles himself serious lands and armies.
