Here is what I've seen in practice. First, you will need to gross up the net payroll for the taxes. Since the employer is paying these, typically the gross up in wages is only for the FICA/Medicare taxes. The amount of $300 is small (as compared to annual wages), omit any withholding for Federal, state or local income taxes. The amount will be included in wages on the W-2 and reduces the employees refund or increasing the amount due.
Though you are not withholding any income taxes. I am not aware of a case were the IRS is concerned with withholding taxes on small Christmas bonuses. If the bonus was over 3% of an employees annual wages, it would be a different matter,
The attached is a spreadsheet to calculate the FICA and Medicare taxes for a given desired net pay. If an employee is over the FICA limit, omit FICA in the wage gross up. You made need to include a local payroll tax in one is assessed.
Enter the payroll in MAS with manual taxes and no deductions. Enter the gross wage amount and the amount for FICA and Medicare when prompted. Make sure that the tax amounts are entered in the correct boxes. Just FICA and Medicare. Also turn off direct deposit. These are usual checks that are handled out.
Technically withholding for income taxes are referred to as withholding taxes. FICA/Medicare and in some cases unemployment are payroll taxes.