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Okay, this is gonna be a strange question.
The character just says out of the blue (in order to lighten the mood) :
ハナクソの秘密をそっと話{はな}くそう!! [with dots above the seconds は、な、く and そ]
Is it just a pun on 話そう？ => Let's talk discretely about the secret of the snot!!
Like, I don't know, if there was a verb "to sno" in english meaning "to speak" and the speaker voluntarily pronounced it "snoT" instead of "sno" : Let's snoT discretely about the secret of the snot!!
Grammatically correct would be 話そう, without the く. But in order to make it similar to ハナクソ (similar words tend to be funny, right?), only one single hiragana く is added. Your analogy in English fits this perfectly. The く functions the same way as your T in snoT.
