Give them another two weeks. Sometimes brown isn't dead. When it is obvious no new growth is going to come along, cut off the dead bit.

I'd do it now. It becomes very difficult to cut out the dead canes when there is too much fragile new growth around them. I started pruning mine a few weeks ago. You want to cut out anything dead. The easiest way is to look for green cane and go up the cane and cut where the green starts turning brown or black. Make sure any black areas on the cane are removed when you prune as that is canker. You need to cut below the canker before it can spread.