I wonder, what it is? To me it seems pretty unlikely that it is to get Hanai - unlike hwat she is saying herself. The reason to not belive her words is her personality - she seems to be pretty much of a fox, what she showed in chapter 190 when talking to Eri about her relationship with Harima, - and the way she is carrying out her "resolve" to start dating Hanai.
Sanding Yakumo is a really bad decision - if we assume that she really wants to get Hanai - it is like giving the main enemy all the advantage. It is much simplier to put letter in his shoe box or to give it herself. I'm sure the last one will work, unlike what she is saying - Hanai is gentle to girls and will never turn down anyone without paying attention to thier troubles - such a heartless act is not something a true president of a council would do after all. And Inaba already has an experience of successfully geting near Hanai - when she asked him to help with her homework (forgot what chapter). So it won't be hard to do the same one more time. But, instead sheis sending Yakumo. The question is - why? Does she want them to pair up, or does she want Yakumo to reject him, or maybe her desire is to look at a couple of funny scenes - like Akira always does?