I am considering purchasing an "Air-king" as supposed to a "DateJust",
but apparently this model is not a chronometer.  Should that be a
concern in my purchase decision?  Is the DateJust significantly better
that the Air-King as far as keeping accurate time?  If I do not have
to pay for the date option, I rather not.

This site tells you that a new Air-King can be adjusted to +/- 3secs/day.

http://www.watchseller.com/rolexairking.html

This is the best-case situation, of course, but "chronometer"
accuracy, as this site explains (and also that such accuracy is not
necessary for every day use):

http://www.chronocentric.com/watches/accuracy.shtml

If you are considering buying an older watch  - which is a valid
option -  I would suggest buying from a dealer who can confirm that
the watch has been cleaned and confirm its accuracy.  With older
watches, be careful to check that the screw-down crown really screws
down properly.  The threads get worn from daily winding.  Maybe it
catches on the last bit of thread when you see it in the store, but
then later won't.  I have one like that. Bah!