I ran a simple simulation in R:
> p = 0.5
> v = rbinom(n = 1000000, size = 1672, p)
> v = v/1672
> mean(v >= .5633)
[1] 0
So, the estimated p-value is 0 (or p < 0.001).
I also estimated the following based on 21% unsigned ballots: 7,962 people who cast a vote, 6,290 of those people signed their ballot, and 3,152 of the signers casted a NO vote. If those estimates are close, then if you combine the NO votes from the signed (3,152) and unsigned (942) ballots, you have a NO vote cast by 51.4% of all voters.
The 3,152 NO votes is a rough midpoint of the possible range of NO votes from signed voters that would round to 50.1% (3149 to 3154 votes). A range of possible percentages for NO votes from all voters (signed and unsigned) would be from 51.38% to 51.44%.
Bob