Add widget to a page dynamically

Hello dear WP developers,
I am developing a widget that must be added to a page selected by the user dynamically. Well, I am not sure how to do this so I was thinking whether it would be a good idea if I create a filter plugin instead of a widget that would replace <calculator-interface> with the web form. Is this a good practice and will it work with all themes? Should I create put the interface in a different html file and replace <calculator-interface> with an iFrame that links to that file for cross theme compatibility or is there a way I can allow user to dynamically add widget inside a page. Whatever solution you suggest, please keep in mind that I do not have access to the clients WP so I have to do everything dynamically. I will just send a WP plugin and he will configure and add it to whatever page/post(if possible or only page) he wants.
Please go easy on me because I am new to WP-plugins and widget

Thank You