Give it a try! I think all the WW centers are set up basically the same way, but like anniet said, it might be a little different if you meet at a church or other meeting place.
They are VERY discreet. One of the things that is really BIG with WW is when you lose 10%. The first time you weigh in, they mark on your card how many pounds you have to lose to lose your 10%. At that meeting, you get special keyring and they make a big deal out of you. BUT they NEVER say how many pounds you lost to get to that 10%!! (And I'm sure that if you feel uncomfortable, they will be glad to give you your keyring privately, and NOT make a big deal out of it, if you ask!)
The same week I hit my 10%, I also passed a 5-lb. loss marker. This is also usually celebrated at the meeting. My leader gave me my 5-lb. star privately before the meeting started, so that she could give me my keyring at the meeting.
I think a lot of people begin WW with feelings similar to yours. But I've been told that when they see how positive the meetings and reinforcements are, they lose a lot of the feelings of embarrassment and are glad to have the honors!
Good luck. I do hope you'll give WW a try.