HIH-4000 maximum voltage in concern
Yes, you do need to worry about the extra .2V.  Silicon vendors put some guard band in, so your device would likely work, but you could see erratic operation and you could experience reduced lifetime.

Jim's suggestion of putting a diode in series would work, but I would use a Schottky, since you only need .2V of drop it would give you longer run time.

You could also look at using a buck-boost converter to supply the 5V.  That would let you get 5V out over the whole battery discharge curve and use more of the full energy of your battery. (Though by 0.9V the batteries are pretty much dead, so not sure how much extra run time that will give you or what voltage the rest of your circuit needs.)