This is what I would do.
First I would add the new value without removing the old value
Then I would add an acf/load_value filter for the field. In this filter I would loop over the values that are already set and replace the old value if it exists with the new value.
Then I would delete the old value from the field.
At this point I would ignore it. When the user updates the new value will be set and until then the old value will be replace with the new value.
On the other hand if I set up it us using value and labels in the field settings like this
value 1 : label 1
value 2 : label 2
I would change the label end ignore the incorrect spelling on the value
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