There's a nifty Safari Extension called Awesome Screenshots that makes taking and editing screen shots so easy and quick even I can do it. One feature is a "blur" that you just paint on using trackpad or mouse.
Really, check out this Extension - I think it's terrific. Everything you could need for screenshots in one place.
(No, I don't own stock in the dev!)
But if just blurring is used, people can find out your sensitive info, no?
It depends on the blurring. Simple gaussian blur where you can still more or less recognize individual characters then perhaps yes. But if you "pixelate" the section or draw an opaque rectangle over it or blur it to the point it is hard to tell there was writing there in the first place then no, nobody can recover the information. Unlike optical or photographic blur, software blur can destroy information that would be required to "sharpen" an image if the blurring is severe enough. Pandora and other streaming services use 128 KBPS streaming audio. Once it's at that level, there is no real way to "enhance" it back up to the quality of a lossless 256 KBPS. The same is true for images. Make it so blurry you can't count characters and it will be impractical for anybody to reconstruct your info.
Here's a puzzle for you. Go ahead and try to get my "personal info" from the following blurred text...