What type of hydrangeas are they and what zone are you in? If you plant them in pots you will need to water them a lot more often than if you stick them in the ground.

I would find a temporary spot for them where they can grow until the fall when you can move them again. If they are paniculatas they will bloom fine moving them at this time, if they are mopheads they may not bloom this year depending on the variety. I did get one move last year pretty late and it still bloomed (3 years old too) but it was a reblomming Endless Summer.

Maybe someone else with more experience with potting them up might be able to give you advice on that.

How large of project, or rather, do you know approximately how long the renovations will take?

Some advice here from another similar question just several days ago...

Here is a link that might be useful: Moving hydrangeas home repairs