One technique is, do it with Custom Fields. Create the custom-field with the Key “Category 1 paragraph” and the Value, type your paragraph.
Then use the WP code for getting a custom field value. It’s shown in the Codex or you can use Get Custom Field Values plugin to do it with 1 line of code to insert in your theme (on the single post template). You could do it with Conditionals if you have different categories with a different custom field for each.
This way, each time you need to change that paragraph, just go into a newer post and put a new value for that custom field.
This method will take a bit of work on your part, not quite as simple as a basic plugin. There may be another way.
Another possible thing to look into is the Awesom News plugin. It gives you a replaceable paragraph on your homepage, might be able to use it for single post pages.
I was looking around and I found this plugin, that I thought might help you.
http://www.dcoda.co.uk/downloads/wordpress/wp_boilerplate/
Only problem is I’m not sure if you need to insert the code for this plugin inside the Post. If you can just put it once in your theme’s single.php that would be better probably for you, so you don’t have to go back to all those old posts.
Well, maybe something to look into