There are plenty 'web based ssh' tools. Use this search term in Google and you get Java, php and C based tools all capable of being integrated with your Apache webserver. Some are really easy to install.
The BIG security issue is not whether you're able to destroy your server, but the real security issue is the fact you open your server with ssh access on the browser port. Your dependent on several components now to make sure your server does not get hacked.
I would never allow such a tool on my servers on the public internet. But of course, it your server. Be really sure your box remains closed.