I don't think any Hydrangea will survive full shade - maybe an oakleaf - I don't have experience with those. Most like morning sun, afternoon shade but with a good watering schedule may do ok in the opposite conditions. I would recommend a paniculata as they are the most hardy in afternoon sun. They can also get quite large and may fill in your area enough where one will be sufficient rather than 2. The limelights are my favorites but there are several others. Pink Diamond and quick fire are another two I have that so far are doing very well. These are the variety that start whitish/green and fade to pink not the blue or pink ones. You can underplant with some hosta that will do well in the shade for you.
Best of Luck!

With your sun situation any of all paniculatas will be the right choice.
How big is the 'large empty corner'? Most of paniculatas are large shrubs, say 8x8' and larger.
Even if you plant one plant behind another it doesn't meant that one of them will be completely shaded by another. In this case you simply should prune frontal plant every year to 3' while leaving back one as is. In such case I would of choose cultivars with different bloom time, say Quick Fire (blooms in early July) in front and Limelight or PG (blooms in late July - August) in a back.

Thanks jemboysch and ego45! Paniculata it is! If it gets 8' x 8', that will be plenty big to fill my space.