Make your own PHP script which will do the final formatting and redirection to the proper url, because the input fields also vary depending on the search engine. For the least, I wouldn't rely on JavaScript to change the field attributes depending on the selected search engine; I for one use NoScript extension by default, thus it would be frustrating if the search didn't work. With a PHP script there will be no problems.

Also, be careful with character code pages and encodings! Wikipedia takes UTF-8, Google can take UTF-8 or ISO-8859-1... so if your page's content encoding isn't UTF-8, you need to use utf8encode() in the PHP script (and even then it might not work 100% correctly). Although I highly recommend using UTF-8 as the default page encoding, less problems with non-English characters overall.