There is currently no easy way to do this, or even a mildly difficult way for that matter.
I have heard that some people are working on crossword widgets, but I haven't seen one in the flesh as yet.
OK. Again I am not needing clarification here. Did you INSERT the SWF as an animation into the Captivate project? Or, did you keep the SWF as an external file? If the SWF is external to the main Cp SWF then perhaps it's not working when you publish because the content cannot find the SWF. If you have made sure that the SWF is definitely in the publish location, check whether or not you have that location set as a trusted location in your Flash Global Security settings.