Urethane, epoxy, probably a few other glue systems are non-solvent based, and don't give off (very) toxic fumes as they cure (sorry for the weasel words, but without a definition of toxic, they need to be there). The problem with the urethane and epoxy glues is that the un-cured parts of the glues can be quite toxic (both to workers or to the environment in case of spills). You could consider natural glue systems, e.g. hide glues...completely natural based...but you have to go through a lot of horses to make it. There are hot-melt polyester adhesives that are pretty non-toxic, but I hate when the stuff drools onto my fingers, ouch!
Regarding the specification, are you talking about this one:
Found it at the top of a google search...
From 5.2.3(d) in that spec., it would appear that you want an adhesive with less than 0.5% formaldehyde content.
The remainder of the spec. requirements for adhesives is in section 5.2.12, and I agree it is pretty vaguely worded. Mostly, they would be reviewing the MSDS for the wet glue, and be looking for VOC's and carcinogenic chemicals. I would think urethane 2-part adhesives would be able to meet the requirements, possibly some of the acrylic adhesives, and likely silicone adhesives as well. You should contact adhesive suppliers (National Starch Co, 3M, Devcon) for glues that meet your needs, then look for low-toxicity versions of them. 3M makes a product, for instance, called 3M™ Fastbond™ Water-Based Adhesive, that I found in a about 60 seconds of browsing on their website. Whether any of these would work adequately for your furniture, I couldn't say. Good luck!
