If you want to sing a lot of the good old songs are in Waltz time.
My Bonny lies over the ocean.
Skye Boat Song, Ca the ewes, Westering home or I love a Lassie (if you can include Scottish).
Daisy, Daisy; She was a sweet little dickie bird; Two little girls in blue (as a set).
You are my honeysuckle.
How much is that doggie in the window (popular in England in the 50s, might have been written by an American for all I know).
Star of the County Down (probably an English tune, but the Irish words are better know).
All round my hat.
Polly Oliver.
etc.etc.
There seem to be a lot of Irish songs wishing they were back home in --- which callers sing for waltzing, between Irish Set dances.

I've just reread the first post. Do you want it for free waltzing are you calling something like Circle Waltz. My preference for that would be a 32 bar tune (Scarborough Fair is 16) as the dance is in 2 16 bar sections so you keep the partner you've got when the tune changes.