On the PWCC side, we generally recommend against planting/transplanting anything that’s susceptible to winter damage in fall. In colder climates (zone 4, 5, even parts of 6), bigleaf hydrangeas can definitely experience some serious winter damage. However, oakleaf hydrangea pretty much never gets severe winter damage even in zone 5, so I would think it would be okay. That said, if they are located in zone 7+, I’d say go for it, you’ll be fine. If they’re in 5 or 6, they’ll probably still be fine with an oakleaf but would want to do it sooner than later, and would definitely want to get a good layer of mulch down over the roots after moving.