I've just retired from a 40 year career related to safe use of chemicals, both in industrial and laboratory settings. After reading all of the punditry posted above, I would say that @
cyccommute has the best handle on the reality of functional effectiveness and safety, though there are a lot of subtle factors related to a particular chemical's properties other than toxicity that affect the hazard of use.
The bottom line is that low volatility, high flash point mineral spirits (a generic hydrocarbon product available by many names) provides an excellent balance between effectiveness and hazard. Use as little as necessary and don't run away from a bit of elbow grease.
Limonene-based products work ok as well and are low hazard, but have a tougher time with hardened grease. I've always been concerned about residue on bearing surfaces, though.