Hi,
You can develop your custom
inline controls for those and take the inspiration/code logic from the search web parts (placed in the CMSWebparts folder).
However, it does not make any sense to me - you want to add the search boxes into, lets say, every editable region? What about all the settings for the search? I have never seen this and right now I do not see any advantage of using them in this wayl
Best regards,
Juraj Ondrus