OK, there's absolutely no information for Singapore.
For the country in which the vast majority of Sikhs live (India), there's a one-line reference to article 25 of the Constitution, but no specific information on practical stuff like wearing kirpans on airplanes.
For Canada, it says "In most public places in Canada a Sikh religious Kirpan is allowed but there some places where it is not clear cut such as workplaces and schools." Makes no mention of the fact that small kirpans are now allowed on airplanes in Canada.
The website shows less information than you'd get on the first page of a Google search.
1. All of the answers at the link above are written by ethnic Chinese on a general basis regarding bearing of weapons. The mainstream Singaporean does not know of specific accommodations for Sikhs in Singapore.
The Sikh community has come to an accommodation with the police, as stated above.
If you're going to Singapore, you won't have a problem, just keep your kirpan out of sight. Also stitch your gatra really tight so the kirpan doesn't fall out of the gatra. And don't talk about your kirpan. What the mainstream community doesn't know won't hurt them.
If one of your co-workers asks about Sikhs wearing kirpan, just tell them you're supposed to wear a kirpan, but you follow all applicable laws while in Singapore. Don't make problems for our brothers who live in Singapore.
2. If you still have doubts, you can call one of the phone numbers for the Sikh Advisory Board, or call any of the Gurdwaras of Singapore, but they'll tell you the same thing: wear a small hidden kirpan.