darkwingrubberducky

If by unique you mean the veridian blade, the green/silver one, yes you can get your very own. Either by looting the museum or helping the Queen in Iziz or by doing the "opening new trade routes" sub quest on Nar Shaddaa. Eg, helping the rodian saleslady.

When you first speak to the Handmaiden you have an option to ask about Atris. And then she asks about Jedi falling in love, getting married, keeping it a secret... One of your potential responses is: "I believe it's called pulling a Bindo." That made me chuckle.