How dangerous is superglue?
You should not regard this answer as medical advice. If concerned about your health consult a physician.

The glue you link to (TAMIYA  EXTRA-THIN  CEMENT, made by IKEGAMI PAINT INDUSTRY COMPANY), according to a material safety data sheet (MSDS) I was able to retrieve online, appears to be a 1:1 mixture of acetone and butyl acetate. Such a mixture works in a similar way to dihloromethane as a solvent to weld together plastic parts. Quoting the wikipedia, 


  Acetone is believed to exhibit only slight toxicity in normal use, and there is no strong evidence of chronic health effects if basic precautions are followed.


OSHA classifies acetone under the following health codes ("principal effect(s) of exposure to each substance [...] used in determining if a violation of an air contaminant standard is serious"):


  HE16     Irritation-Eyes, Nose, Throat, Skin---Mild


OSHA classifies butyl acetate as follows:


  HE8    Nervous System Disturbances---Narcosis
  
  HE15   Irritation-Eyes, Nose, Throat, Skin---Moderate




For completeness, I include a screenshot from the beginning of the MSDS I found for the adhesive. For more on the GHS classification (divisions or categories) you can refer to the method employed in classifying substances.