As long as you can sign transactions you can use any client that supports it.
The Mastercoin-wallet software just does all this for you so you don't need an other (Bitcoin) client.
Ahhh, okay so that website did throw me off a bit. The last thing, hopefully, is getting the private key. That's where I was a little thrown off by that site, do I need a bitcoin client to generate a private address for me?