After trying some extensions, I found that Pixlr Grabber does exactly what I need: simply capture parts of webpages and share them. Period. It does what we were used to do with the Snipping tool, but way more effectively.
With Pixlr Grabber you can edit, save and SHARE.
If you use Pixlr to grab pictures for your blog (Blogger), be aware that the url of the screen capture not always work. Right click the capture and choose "copy url of image". Then, paste the url in the box "add image from the web".