There isn't any battery recycling need in Singapore because the importation of primary batteries (non-recyclable) has been restricted to the lowest possible content of toxic metal such as mercury. See two articles giving great explanation of the scenario in Singapore and also how we can do to minimize wastage and pollution. (1) recycling batteries in Singapore, (2) Efforts to recycle batteries - part II.
Lithium ion batteries from phones and notebooks are recycled in Singapore but the collection centers are available only at certain areas. Lithium is toxic and a teratogen. However, the material safety data sheet (MSDS) pertaining to lithium ion battery states that teratogenicity and reproductive toxicity are "not anticipated". I could mean that no data is available and no toxicity is expected, or preliminary data shown that toxicity is not anticipated, or preliminary data on animal shows no anticipated toxicity in human.
My main problem with batteries is that some are prone to leaks. The leaked fluid often damages sensitive gadgets. Although the content of batteries is stated as non-toxic, but there is always a possibility that certain individuals will be susceptible to allergic reaction to the content.
I have tried Duracell batteries (Made in China) that leaked afterwards and damaged my mouse. I have tried Panasonic batteries (Made in Thailand) that also leaked and tainted the stroller fan. I bet most batteries out there are prone to leakage.
So far, I have not experienced leaky recyclable batteries. It seemed that the exterior of these batteries are different from primary batteries (non-recyclable; they are recyclable up to 10 times with certain charger).