Well, to cut to the chase, the answer is 'Yes we can!'.
The day dawned bright and clear, so we set to removing the old shower panel and frame and fitting the new one. We took it step by step and were able to reuse the existing runners screwed into the walls which saved one tricky job of drilling into the tiles. The new frame was the same size as the existing one, so we knew how much to cut off at the bottom to get it to fit into the shower tray, and everything slotted into place very neatly. We had more or less finished and tidied up by lunchtime, so now we have a clean, freshly decorated and non grotty bathroom, which seems a minor miracle after seeing it full of broken glass last weekend.
In other news, I had a remarkably vivid zombie apocalypse dream last night, in which I was part of a team investigating a secret military base that was the source of the infection. It was pretty gruesome but strangely satisfying to let rip with a pump action shotgun at the oncoming undead hordes. Perhaps I need to play some Left 4 Dead?