OH OK your OP does not only indicates that your wheels are 6spd hence your shifters may or should be 6spd. you did not mention that you were changing the whole drivetrain.
you may need to respace and then redish the wheel slightly.
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“One morning you wake up, the girl is gone, the bikes are gone, all that's left behind is a pair of old tires and a tube of tubular glue, all squeezed out"
Sugar "Kane" Kowalczyk