Safety when handling cyclohexylamine in non-industrial amounts
I once did some work with some small chain alkyl amines and they were bad news.  They would actually burn you if some got on your skin.  I always used a respirator and worked in a hood when using them.


  as long as I don't feel irritation of my lungs or eyes, am I safe?


If this is a one time occurrence, given the small quantities, I'd say the odds are way in your favor, but they call it "odds" for a reason.  My advice would be not to do it again without a respirator and hood where the exhaust is treated.


  And if I do, is there enough time to clean up (i.e. the most essential
  things, like shutting off electricity and closing open jars of
  chemicals) and leave?


If you ask an industrial hygiene professional, I'm sure the answer would be "no".  If it were me and I just began to notice some very mild sensation, I think I'd hold my breath and try to shut things down.  I know it doesn't make sense, but that's what I'd do.  If I noticed anything beyond the onset of very minor discomfort, I'd clear out fast and call the fire department.


  Finally I accidentally touched a drop of cyclohexylamine (from the
  pipette) when I was cleaning up, with no gloves on.


I'd keep washing it every so often during the day and I'd put some burn cream on it in between the washings.  I'd also take a good shower.  No harm in overreacting.


  still haven't figured out if I can pour the diluted mixture of water
  and cyclohexylamine down the drain


I'm almost positive that the answer is no.  Besides you and the neighborhood, it might react with the pipes or what's stuck in the pipes and create longer term toxicity problems when you're in that room at some later date.   Where I live, we have hazardous chemical drop-off centers (mainly for paint, oil and household chemicals, but used for everything chemical).  I'd pay the relatively small amount they charge and drop it off there.

One final note, even when using the right protective gear, some people become "sensitized" to amines.  This means that future exposure at even lower levels to a wide array of amines can be more dangerous.  Also, I'd try to open up the exposed room to as much outside air as possible, use a room fan too if you have one.