I have the same concern monblu! my husband saw the picture of lindsey lohan (geez, what DOESN't she have?) with the Yris Muse which comes with a thin shoulder strap. He's not a bag person AT ALL but I guess he loved the bag. Odd isn't it?
So we made a trip to midtown manhattan YSL to check out if they had it anymore. The 2006-2007 muse bags do not come with straps at any size. And they don't sell it on the side or seperately either. They no longer make or have the Yris at any stores in the united states (except a canvas one at some mall??). (yeah, we made some calls. =) Anyways, I hope this helps.
Personally, I'm waiting to get a muse until I can decide for sure which size/color I really want. And I think your color, chocolate, is absolutely gorgeous.
Good luck!