I had WebEngine set up to preview pages in Safari. But now Safari's stopped working, and when I hit preview, nothing comes up because Safari's not working. Is there any way to change the program previewed pages appear in?

I think you might find the answer in this thread.

I tried the first thing, but it's not working. How does one "drag" a page into an internet shortcut?

If you have a shortcut to another browser on your desktop you can open Windows Explorer, find your html page you want to see in the browser left-click on it and hold down your mouse then drop the file on the shortcut.