Wa Alaikum Salam,
If the beard grows on only one side, the other side is only permitted to be cut off (not shaved) upto an extent where both sides are equal.
The reason stated in the question is not enough to shave it completely. It would still be Haram.
The side which grows slower should be left untouched until it exceeds one fistful in length. The other side could be made equal to the slow side as and when needed as long as the slow side is left untouched.
And Allah knows best
————————————– Maulana Muhammad
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