More like the other way around. Sasori's poison
does not mix with water [
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]-[
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]. As you can see, it is clearly very distinguishable within water, so the chances of Kisame willingly taking it in is around zero. Additionally, Sasori getting caught within the WD ends him. The water will seep and soak in his wooden body, which will slow down his movements. Kisamehada is also actively absorbing chakra, so manipulating a puppet with chakra strings isn't happening either.