Since your baby boy is born in Singapore (SG), you need to register his birth with the Registry of Births and Deaths at the Singapore Immigration and Registration (SIR) office (
http://www.sir.gov.sg/).
By registering his birth with SIR, your child does not automatically become a Singapore citizen. Only children of Singapore citizens can be Singapore citizens at birth.
If one of the parents is a Singapore citizen (in this case, your wife) and the child is born in Singapore, you need to be very careful with your choice. I am quite puzzled that you are given a choice. By SG law, your child should be an SG citizen by birth. It does not apply if both parents are British citizens, as some here have pointed out. However, the law is very specific in that it addresses the male child, whether he is born in SG or overseas, as an SG citizen if he is born to a father who is an SG citizen by birth. So, perhaps, in your case, you are given the choice since you are not an SG citizen despite the fact that your wife is one. (The SG law is gender-biased here.)
In the context of National Service (NS), here are the rules of SG law (taken from http://www.mfa.gov.sg/consular/faq/citizenship.html on the question "Who can renounce their Singapore citizenship?":
"Since 5 Mar 79, the Government has been empowered under Article 128(2)(b) of the Constitution of the Republic of Singapore to withhold registering a declaration of renunciation by a person who is subject to the Enlistment Act unless he has:
- discharged his liability for full-time NS;
- rendered at least 3 years of Operationally Ready National Service; or
- complied with other conditions laid down by the government.
For male citizens who left Singapore before the age of 11 and have not enjoyed significant socio-economic benefits in Singapore, i.e. have not applied for an NRIC, extended their Singapore passport validity beyond the age of 11 or studied in Singapore school beyond 11 years old, we will not object to their renunciation of Singapore citizenship if they do not wish to fulfil their NS obligations. However, they should still register for full-time NS with CMPB at the age of 17½ and apply for deferment from enlistment till the age of 21 (under Singapore law, a citizen could only renounce at the age of 21) pending their decision on their Singapore citizenship status. Those who subsequently renounce their citizenship at the age of 21 will not be required to serve NS. Those who retain their Singapore citizenship will be enlisted for NSF.
Generally, those who left Singapore after the age of 11 will be deemed to have enjoyed the socio-economic benefits of Singapore. They will not be allowed to renounce their Singapore citizenship without fulfilling NS obligations."
In the context of dual citizenship, here is the excerpt from the same url:
"It is not our Government's policy to allow dual nationality. Any Singapore citizen who has formally acquired the citizenship of another country may be deprived of his Singapore citizenship under Article 134 of the Constitution of the Republic of Singapore."
In the context of renunciation of SG citizenship, especially when it is related to males reaching 21 years of age, here's the excerpt:
"A Singapore citizen over the age of 21 years and of sound mind and who is about to become the citizen of another country may apply to renounce his Singapore citizenship.
However, the Government may withhold the registration of a declaration of renunciation –
a) if the declaration is made during any war in which Singapore is engaged; or
b) if the declaration is made by a person subject to the Enlistment Act unless he has
discharged his liability for full-time service under section 12 of that Act;
rendered at least 3 years of reserve service under section 13 of that Act in lieu of such full-time service; or
complied with such conditions as may be determined by the Government."
Considering all the above excerpts from SG law (and regulations), there are catch-22 situations when your child reaches 11, 17½, and 21 years. If your child is registered as an SG citizen at birth, which is possible by nature of your spouse's SG citizenship and the child's birthplace, he will be required to register for NS at age 17½ and seek for deferment from NS till age 21 when he is given the choice to denounce his SG citizenship, i.e. if he has opted for or is already a British citizen then. Of course, the Age 11 criterion plays a role here if you decide to leave SG before he reaches his 11th birthday. But once he is registered as an SG passport holder as a child (i.e. an SG citizen), he is liable to fulfil the requirements of the Enlistment Act even though he may spend most of his life (Age 11 criterion) outside of SG. The unknown (and risk) is that the SG authorities may turn down his renunciation request at age 21 if he failed to comply with the Enlistment Act requirement of registering for NS at age 17½ and seeking deferment from 17½ to 21 years. That he may be required to return to SG to serve full-time NS at the age of 18 is another point of concern for you, i.e. if his deferment application is unsuccessful.
Simply put, the 17½ to 21 year period of his life is in SG legal limbo if he is registered as an SG citizen at birth, even though he may be holding a British passport before or after age 11.
Although SG law does not permit dual-citizenship (as indicated above in one excerpt), it contradicts itself or more appropriately makes itself contradictorily-convenient by word-craft and subtlety to hide the fact that a male can effectively become both a citizen of SG and a citizen of another country up to the age of 21.
Hope this helps.