During dormancy would be best if you must.

Back fifteen years ago I transplanted a crepe myrtle that I guess was 4 or 5 foot tall. What a pain. New ones were just $20.

You could cut the hydrangeas to the ground then paint the stumps with a herbicide. (Paint not spray.) The hydrangea roots will just rot in situ. You could take cuttings before chopping the shrubs down. But what is the rational for getting rid of them?

Both are shallow rooted so it depends on how much root growth there has been and if the roots are commingling. Water all the day before moving. Prepare the new planting holes before moving the hydrangeas. You could inspect for roots from both mid way between both to see if you run into a lots of roots or not. So dig carefully, especially if you detect roots and try not to disturb them too much. If you encounter resistance, stop and dig further out to avoid pulling on the roots. As you lift the hydrangeas, inspect the area for any roots belonging to the sugar maple. When done, cover any exposed roots from the maple well using organic compost or garden soil. Mulch both well when done and water as soon as the top soil is dry. Monitor as if the shrubs were just planted new, especially during their first summer months.