Although i think this isnt fair because the sharigan is part of sasuke's genes ill still go by your rules.
Alot of people are underestimating sasukes speed and his skill. Anyway ill tell you why sasuke still has the upperhand and can win even without his sharigan.
First and foremost sasuke's is speed in shuppuden is 4.5/5 same as kakashi's and believe it or not same as rock lee.
Sasuke:
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Kakashi:
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Rock lee:
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In series one sasuke had the sharigan and could see lee's attack but didnt have the speed to react therefore his sharigan was useless. In this case its the opposite because he has the speed, but not the sharigan.
Also people are forgetting that lee can only use taijutsu, whilst sasuke can use both taijutsu and ninjutsu. Granted, due to the nature of chidori, although he can still use the technqiue its too risky without the sharigan, but he still has other lightning based attacks to use and fire based attacks.
Not to mention chidori nagashi would prove very useful against a taijutsu user since they would obviously want close combat.
Also if lee decided to use his gates which he would, if that isnt enough to defeat sasuke he is a sitting duck due to the side effects of using the gates. Thats when kirin comes in