To my understanding, your wife cannot use the public health service unless she has been issued a HKID card. The cost of a private delivery in a public hospital cannot be refunded unless your wife is issued a HKID card before the delivery.
Giving birth in a public hospital can be just as expensive as in a private hospital unless you have the HKID. According to the hospital authority website the minimum charge for non HKID holder is $39,000, but you must have registered prior to birth. If you just show up on the day of the delivery you will be charged $90,000. See: https://www.ha.org.hk/haho/ho/cs/v3/serviceguide_feenchg-en.htm
If I was you in your shoes, i would find a private hospital ASAP. Have you called around the hospitals or looked at their websites? From this list of hospitals, the cheapest private package is at Precious Blood Caritas around $14,500 - Private Hospital Maternity Packages in Hong Kong 2015 - Hong Kong GeoBaby
Giving birth in a public hospital can be just as expensive as in a private hospital unless you have the HKID. According to the hospital authority website the minimum charge for non HKID holder is $39,000, but you must have registered prior to birth. If you just show up on the day of the delivery you will be charged $90,000. See: https://www.ha.org.hk/haho/ho/cs/v3/serviceguide_feenchg-en.htm
If I was you in your shoes, i would find a private hospital ASAP. Have you called around the hospitals or looked at their websites? From this list of hospitals, the cheapest private package is at Precious Blood Caritas around $14,500 - Private Hospital Maternity Packages in Hong Kong 2015 - Hong Kong GeoBaby