I wanted to do this on a few blogs because sometimes you just need to see exactly what is going on with how your blog looks. I agree, that the screwdriver and wrench icons in blogger blogs are handy for on the spot editing of added gadgets but they do however interfere with the actual spaces between sidebar gadgets and what not. The only way you can view your blow how everyone would see it would be to preview it or to log out of blogger and then see your blog. What if you just never want to see the icon at all... well I read an article on Blogger Tips And Tricks that had the solution to removing the screwdriver and wrench icon.
Here is the link to the article:
Removing Pencil And Screwdriver And Wrench Icons
You will also find a tutorial on removing the quick editing pencil icon. Though I never found a reason to not want it yet. I find it very useful. I guess it's always best to have options.