It's will be difficult but i think kakashi would win this,if that scenario of fight would happen i can't believe that kishi would make kakashi die against a character such as sasori who use poison.
a sharingan/byukugan user would be bad thing for sasori because kakashi will imediatelly see anomally with his chakra flow that come from his only human part ,his core.
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he can't miss it.please don't bring me about kakuzu's hearts ,kakuzu isn't a puppet and his chakra doesn't come only from his heart so he would be able to have a regular chakra flow like everybody and it's never stated that kakashi didn't see or not ,he attacked the main heart and could been the main one ,sasori has all his chakra from his core only,that impossible for a sharingan user to not see this.
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kakashi already know about sasori and his poison ,you decided to gave the kamui knowledge to sasori but whatever that doesn't change anything to the issue of the fight ,he will do better than chiyo and sakura (chiyo was puppet master but that doesn't mean anything about dodging skills and moving ,if sakura and chiyo were able to do it, there is absolutely no doubt that kakashi will do even better ,he has sharingan and is extremelly fast and move very well (stated by tobi and nagato) .dodging don't take him much stanima ,so that way he has a good endurance but i doubt that this fight will dure longtime.
be sure he will detect it as soon as the fight start ,now his only problem is to get close to sasori,he has many ways to do it, like doton underground ,he can stay anytime and make diversion from underground with a raiton kage bunshin and if he let himself stab by sasori with that raiton bunshin it's done for almost sasori ,he won't be able to move and will be paralysed so kakashi will place a raikiri in his heart ,it's his speciality , (notice in this case there is no need to detect his core once,because any ninja would want got his opponent's heart to kill him) .about diversion he can also use hidden mist jutsu so sasori would not be able to control his puppets properly .
finally he can use kamui imediatelly at the start of the fight like against tobi but that would not make it a long fight.
btw i also don't like when people says "why didn't he use kamui vs zabuzu?"or "kakashi never use kamui at start of fight" who are you to decide if he use it or not,kakashi can make his own choice and in this thread we are allowed to use any jutsu anytime against the appropriate characters.if kishi gave kamui to kakashi that's mean he could use as attack(deidera/tobi ) and as defense 'pein,sasuke).
puppets are no match because kakashi will focus on sasori,he would only dodge easily all sasori's attack and focus on him.list me an attack of sasori i'll tell you how kaakshi will dodge it.actually you can't prove my points wrong that are sasori can't detec raiton bunshin,sasori can't move if he get hit by raiton bunshin,kakashi will see his chakra flow from his heart,kakashi is by far faster and move better than chiyo and sakura and got sharingan(you realyse that his speed and move are stated by tobi and nagato).
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