The reason that the find and replace won't work is that the character itself is the same, but Times and Zapf Dingbats have different glyphs for the character, so replacing the character won't do anything, you need to change the style of it instead.
I'm not an MS Word expert, so I don't know if there would be an easy way to do this. I'm pretty sure there is a "paste style" command somewhere though, so you could probably at least go through and do multiple finds and change the font for each character manually.
The reason Zapf Dingbats doesn't work with TextEdit is actually because the Cocoa text system is too smart for its own good. There is actually a separate range of Unicode values specified for the dingbat characters (9984-10175 to be specific). The Zapf Dingbats doesn't have any glyphs in the normal ASCII range, so typing plain characters will cause it to default to the system font. In order to type dingbats into TextEdit, you'd probably need to enable the Unicode keyboard input in the International prefs and enter the Unicode value for the character you want.