It is completely and totally safe to wipe the SSD, as long as you're ok with installing a newer version of macOS, and are able to use a different Mac.
You'll need an 8GB USB drive that you're willing to wipe and a different Mac running 10.6.8 or later.
First, download the macOS [any version] installer from the app store on a different Mac.
While you wait, open Applications/Utilities/Disk Utility on the other Mac. Insert the USB drive. Select he USB drive and press Erase.
Here are the options you need:
Once the download finishes, there are a couple different steps you need to take depending on your version you downloaded.
The following directions are for Sierra.
Open Terminal and enter the following. It is a
sudo command so you'll need an admin password to execute it.
sudo /Applications/Install\ macOS\ Sierra.app/Contents/Resources/createinstallmedia --volume /Volumes/Sierra --applicationpath /Applications/Install\ macOS\ Sierra.app --nointeraction
It'll take about 5 minutes.
Once that finishes, plug the USB into the (powered off) target Mac. Hold down alt/option as you turn it on.
Select your USB labeled Sierra using the arrow keys on your computer.
Now, you have the recovery partition open. Yay!
In the menu bar, open Utilities -> Disk Utility
Select the drive labelled Macintosh HD, and click Erase. Use the same options from the USB above, but name it Macintosh HD.
Finally, quit Disk Utility, and select Install Sierra. Once that process finishes, you're done.