Late July/beginning of August is probably the least desirable time to attempt a transplant :-) But I do understand the time constraints if you are moving.

Ideally, this is something that should be done in the coolest part of the day or one that is overcast. And it is preferable to have the new location already prepared so that the plant is out of the ground for the shortest possible time. An established hydrangea will have a large root system and you will need to get as much of it as possible. It'll be awkward and heavy and may be a two-man job. Current horticultural practices advocate not pruning a transplanted shrub or tree back hard - the theory is it needs all that foliage for transpiration and to recover from transplant shock - however, it is often necessary to trim the plant back some just for ease of moving. Try to leave as much foliar growth as possible while making the plant more transportable :-) And pay very close attention to watering. The plant will no doubt experience significant wilting from shock and there is a tendency often to overwater to compensate. Keep the plant and rootball evenly moist but not wet. If the new home is in a sunnier position, some temporary shade may help.

Good luck!