You should not keep a regularly installed window in a shower. The window in a shower should be a fully enclosed, non-operating vinyl window and you should make sure that it is properly flashed and properly installed. This lessens any chance of water seeping down into the walls creating mold or rotting the walls. It would also be best if you can raise the lower edge of the window up as your contractor recommends to minimize the amount of water that will remain on the ledge after showering. We recommend the Hy-Lite privacy windows for showers.

I agree with the comments above. I would add that a thermal break, fixed glass aluminum window could work as well. I'd also make sure that the tilesetter installs a water-proof membrane at the window sill as one would do at a tiled niche in a shower. The sill should also slope to drain into the shower.

Thank you Deborah, and AMG Architects. Follow-up questions:
The largest window, perpendicular to the shower head, is about 4' wide. We have no difficulty raising the lower edge to the recommended height. The second window has a view, which we'd like to preserve. Can I raise the lower edge to chest height? I have seen lots of pictures that have windows 2' or less off the floor in a shower.
Is there a benefit to using a solid surface window ledge (granite, composite) installed with a slope away from the window, flashed and water-proofed as you describe. Is there any additional benefit from making a more severe slope for the ledge?
Our contractor has said we can use windows that tilt in or out. I can see the wisdom in a fixed pane. What about using a small tilt-open horizontal panel at the top of the small window (farthest from the spray) so that we can get some fresh air flowing?

I think we would defer to your contractor who can see the space and would have a better idea of how your home is constructed. You both need to be comfortable that the water can be controlled properly. It can make a huge mess if water seeps into your walls.

As far as the ledge, what we would do is wrap the window with durock, waterproof it along with the remainder of the shower and tile it. Fewer ways water could get through than putting another product in like a solid surface.

Again, I agree with the comment above in that you need to trust the judgement of the person (people) on site who can see the conditions first hand and are taking responsibility for the installation. Using a solid surface (such as a stone slab, etc.) can slightly reduce the chance of water infiltration but, more importantly, it can provide the opportunity to extend the edge of the sill beyond the face of the tile below to creat a small drip edge. As nice as it would be, I would not install an operable window in this location. Windows are designed to shed water from the outside, not the inside. Install an effective and quiet bath fan on a timer (Panosonic is a good brand here). Minimum slope to drain is 1/4" per foot. More is better but too much slope will look odd.