"Not wanting to" is not sufficient reason not to do something very nearly equivalent (although it isn't converting to seconds so strictly speaking you haven't :) ). Instead convert to Matlab date numbers, plot, then format the time axis as you desire with datetick
doc datenum
doc datetick
Of course, if either
a) the data are evenly sampled, or
b) you don't care about true time spacing if not, then
you can simply plot versus position number and set 'xticklabel' property as you wish. But, in general it is much simpler to "do it right" via datenumbers as outlined above.
