If you're going to insure against the risk that you become unable to work (and unable to earn an income) -- and I think you should! -- then do that. That's called disability income insurance (DII), and there are three carriers in Singapore that sell it: Aviva (IdealIncome), Great Eastern (Pay Assure), and AIA (Premier Disability Cover).
Early Critical Illness, Critical Illness, and Personal Accident insurance are all cause-specific policies, and they are full of holes. That's why they're "cheap." If you're unable to work and to earn an income for any reason(s) not on the list of causes in those policies, you're screwed. I do not like those policies one bit. They don't adequately cover the actual risk you care about: loss of income due to inability to work.
If/when you buy DII, my advice would be to choose the longest elimination period available (6 months is the maximum offered, I believe), and to build up your emergency reserve funds to cover that period of time. That'll help drive down the premium. Also, try to pick something you could at least survive on, and be sure to take inflation into account. For example, if you think you could survive on $3,000/month today, then you'd probably want to choose something like $4,000/month as the payout amount. (I think one of these carriers might offer an escalating payout, so that's another option.) Be very careful to choose the correct job description when you obtain quotations. The premiums are very sensitive to job roles/descriptions.