Sorry to disagree, but the 1-2-3 is usually only for raw beginners to get the hang of it. It soon becomes a bit of a stomp if you carry on like that (think about it).
The waltz should be smoothed out to more like a "one . . two-o-o-o-o-o-o" with the 2 count now encapsulating the former 2-3 (stomp) not wishing to get too technical about it
BTW I'd say the Commodores - 3 x Lady is a good choice.
Be careful when they say a slow waltz. What they mean is slow as opposed to the Viennese twirling thingy. Don't give 'em too slow a waltz timing because that is VERY hard to dance to - unless you've at least got coat tails and numbers pinned on your back, Victor!!!
Shania Twain - Is There Life After Love (from Woman In Me album) makes a beautiful slow waltz.
Now, with regards to:
if it is waltz timing they'll be able to dance to whatever.
With a typical mixed audience, I like to use modern stuff for ballroom/latin requests rather than resorting to
Victor, because I feel it doesn't alienate the younger element.
e.g. requests for a fox-trot - I give 'em "You've Got a Friend in Me" aka Theme from Toy Story

. It actually has a lovely sentiment in the lyrics if you care to listen to them - well suited to Gran and Grandad's 60th anniversary.
or you could use good old Sank Frinatra's "Noo Yoik, Noo Yoik" for a Fox-Trot (but tempo change at the end is a bit of a buggeration factor)
and Cha-Cha-Cha requests get the Mavericks - Dance the Night Away or Shania (again!) - That Don't Impress Me Much, and so on, get the idea?
It keeps younger interests alive much more than Reg Bloody Dixon on the friggin' Blackpool Wurlitzer

they may even join in, in their own way.