The most straightforward way to do this is through the theme layer. Edit the view, and go into the Header option under Basic settings. There, you can put in your custom HTML for the buttons.
However, as you might've noticed, this places the header above the exposed filters, whereas you want the header below them. To do this, go into the Theme information option under Basic settings, and find the Display output section.
There, you'll see a list of file name hints. Create a file within your theme using one of those filename hints. Then, click on Display output: you'll receive the default code you'll need to put within your newly created template file.
You'll notice in this new template of yours that the $header code block is before the $exposed code block. Just switch the positions and save your template. Back on the view configuration page, click on Rescan template files, save your view, and the header you've added will now be below the exposed filters.