One of the many distasteful aspects of National Slavery is the lack of choice of alternative service (AS) - those who are unwilling and/or unable to serve militarily cannot opt out of this (and do something else).
Defenders of the NS Status Quo (many of whom believe that the Country will collapse if any changes at all are made to the current system) claim that if there were a choice of alternative service, everyone would choose it, we would be left with an insufficient number of warm bodies to be cannon fodder and Singapore would be invaded the day after.
It is thus instructive to look at countries with alternative service, and how this has affected their ability to get sufficient military manpower.
Alternative Service in Europe
From European Union without Compulsory Military Service: Consequences for Alternative Service. A comparative study on the policies in EU-member states we can see what alternative service rates are.
For countries with appropriate figures for comparison (Conscientious Objectors (COs) vs serving military conscripts):
From 1993 to 1995 (when conscription was winding down) Belgium had 19,676 doing military service but 737 doing alternative service (AS). That's an alternative service rate of only 3.7%.
In Denmark there are 8,000 conscripts a year and from 1995-1999 figures only a tenth applied for AS.
In Finland only 6% of conscripts become COs.
In France, when they still had conscription less than 3% applied as COs each year.
In the Netherlands at its highest only 8% applied for AS.
In Portugal, for the last year figures were available (1996) less than 10% applied to be CO.
Note that in these Western European countries they are not bombarded with jingoistic messages about the necessity of conscription, it is not part of some sacred national myth, and the politicians do not propagate a crisis mentality.
These statistics also date from the 90s - after the end of the Cold War and before 9/11, when there was no clear enemy in sight and people wanted to enjoy the peace dividend.
Most of these countries are also under the NATO umbrella and can count on the USA to help defend them - and yet very few potential conscripts choose AS.
Finally, note too that Europeans are cheese-eating surrender monkeys - and yet so few of them apply for exemption from military conscription.
So if anything, in Singapore the proportion applying for alternative service would be even lower, and wouldn't significantly affect National Security. This is also without taking into account the fact that many people currently siam (shirk/escape) NS obligations in one way or other, so we can conclude that if there were the option for AS many would take it without significantly affecting military manpower.
Some might claim that military service in Singapore is much worse than in these countries, so the AS rate in Singapore would be higher if there were such an option. Yet, in Russia - where conscription is much shittier than in Singapore, there are few who opt for AS. A cohort has 130,000 conscripts but only 800-2,600 conscientious objectors, so only 0.6-2% opt for AS.
It is not as if European countries can afford to have alternative service because they have no security threats: Finland and Estonia (who have a real threat in the form of Russia next door - a threat that has been very real in the past) also have alternative service (as noted above, Finland had a AS rate of only 6%, and in Estonia from 1995-2001 they only had 11 COs - in 1996, vs 2,652 who completed military service in 2015; a naive division suggests that the AS rate was only 0.4%). I note that Estonia has 1.3 million people and Finland 5.3 million, so their manpower pool is not more than Singapore's (and their land area is a lot bigger so in one frame of analysis, more men are required to defend them).
Greece also has alternative service, despite historical and ongoing tensions with Turkey (e.g. over Cyprus); in 1999 there were "more than 200" COs out of 98,321 - given an average service length of about a year this is about 0.2% (though there're many draft dodgers)
Taking a historical view, I note also that West Germany - on the border of the Iron Curtain and thus a prime candidate for invasion if the Cold War turned Hot - also had alternative service
Alternative Service in Other Countries
We can look, too, at alternative service statistics for a country which actually has real enemies and has actually been involved in real combat: Taiwan (South Korea doesn't have the option of alternative service).
In Taiwan, out of a total of 150,000 conscripts per year, there're 17,000 to 23,000 performing alternative service every year, which is 11-15%.
Another country that comes to mind which actually has real enemies and has actually been involved in real combat is Israel. I trust that not even the most fervent supporter of National Service in Singapore would claim that Singapore's security situation is more precarious than Israel's. Yet, the Israel Defence Forces are transitioning to allowing alternative service.
Thus, it is far more likely that the real reasons why there is no option for alternative service in Singapore arise from political, rather than strategic or military considerations.
It is notable that the prevalence and length of conscription has been declining in the world as countries recognise that it makes neither economic nor military sense (Joshua C. Hall, The Worldwide Decline in Conscription: A Victory for Economics?). Yet, there has only been a small change in Singapore, with the duration of conscription being reduced from 24-30 months to 24 months in 2004.