Crossword Compiler can publish interactive puzzles for the web in just a few clicks. You can use these on your WordPress site, but will need to install a WordPress plugin. Then you can easily upload puzzles from files exported by Crossword Compiler, or import them from a puzzle page already uploaded to crossword.info (using the Web Publish button).
The plugin is also available from the WordPress plugin site, just search for "Crossword Compiler". However due to some site restrictions, the version hosted their does not install the applet file for you, but always uses a remote-loaded file from crossword.info.
When you export the puzzle from Crossword Compiler, you must be using Crossword Compiler version 9/10 or higher (in version 9 you must select the HTML5 option, which is the default).