C) The plant will deal with the old leaves in its own good time.

But .... any canes which fruited last year can be pruned out.

Yeah, blackberries are like grapes in that fruit only sets on green wood from last year's brown wood.

The old canes will not produce fruit anymore, but will instead serve as the backbone for this season's growth (which is what will set fruit). So you can feel free to prune back.

The nice thing about blackberries is that they root very easily from cuttings. If you prune the old cane back, you can always just stick the pruned part back into some moist soil and get a whole new plant out of it.

On caneberries, removing the toothpicks (leafless stems that are just barely hanging onto the canes) is easy and harmless enough, but tugging on old attached leaves can damage the new growth spur or strip a bit of the cane off along with the leaf. Of course you could use a cutting hand tool, but it's not necessary. Clear up here in Portland my blackberries still have half their leaves. Leaf die-off typically begins at the main cane base and works its way up, leaving most of the laterals with overwintering leaves.
The black raspberries have lost all their leaves.

C) is the best choice.

Do option "C", just leave them be. Blackberries are strange... here in zone 3 I lay the canes down and cover them with leaves or straw or soil in late October or early November when the ground is starting to freeze and the snow is about to fly. I uncover them in April when the snow has melted and the garden has dried up a bit. Amazingly, they always have green leaves remaining from the previous season, even though those leaves have been covered so haven't seen a single ray of daylight for the previous 5 or 6 months.

I just uncover the canes, then let the plant decide how much of the cane is going to survive and put out new (fruiting) growth for the new season. Once that becomes obvious, I prune off anything that winter-killed.