If Microsoft\'s method for using IE as a local host for HTA\'s then, can I use any other browser instead?
It isn't so much that IE hosts anything, but that mshta.exe hosts components it shares with IE. MSHTA is a script host, much as CScript and WScript are. While IE is also a script host (in the strictest sense) its primary purpose is to be a Web browser.
The Mozilla project mentioned previously is the closest alternative I have found that is based on a browser's innards.
Other script hosts exist for windows too. One of these is NS Basic/Desktop but it is based on standard Windows controls, not browser rendering and an HTML DOM.