Direct payments by the city to the authority or the organization respectively concerned may be made directly by city warrant drawn upon the fund which is bearing the charge for the employee's wage involved. Such direct payment shall be made whenever, at the discretion of the City Controller and the City Treasurer, it may be deemed convenient and desirable without an intervening accumulation thereof in any special account or fund, notwithstanding provisions in any ordinance prior hereto which direct the establishment of such special accounts or funds, namely §§
53-3B,
53-4B,
53-5B,
53-6B,
53-7B,
53-8B, and
53-9B.