There are two schools of thought here:
if you have agreed with your staff to pay them 80% of their pay during lockdown using the wage subsidy then it could be deemed that agreement covers their public holiday entitlement, and they are simply paid the agreed amount during the lockdown period.
MBIE have advised that employee's are entitled to payment for public holidays during lockdown and pre-COVID19 working patterns are to be used to assess an employee's entitlement to a public holiday. An employer may use the subsidy to pay for the public holiday.
Depending on your payroll system then, you can record the public holiday as taken (at the relevant daily rate) but use the subsidy to pay the amount owing, debiting this from the wage subsidy paid. The result should be the employee is paid the same amount for the period including the public holiday as their normal week's payment under lockdown, with the benefit that the public holiday has been recorded as paid.
Note that if you have to account for the MSD wage subsidy you will need to remember that you have included public holiday payments as part of the subsidy payments. - Go well! - Any queries, feel free to contact email@example.com