When you say delaying is that a fixed delay which in effect is a phase shift. Or is it a micro second extension of the period.
In that case, I would use a presetable counter that normally runs from the same master clock source. Then when you want to change the phase, output the required number to the counter's preset lines and when the reference 1HZ counter makes a transition arrange the preset value is clocked in. I would probably look into using an RS flip flip to handle the request / acknowledge part of this. It is old school TTL logic but it is your best bet for getting the precision you need.Photons can go a long way in 1uS.
do I still need the comparator
or the arduino even?