The New Oxford Companion to Music states: "It is so-called on the assumption that it can be played in one minute - but that is only possible if it is played too fast."
I've been playing the piano for 40 years, and I've never
heard anyone call it Chopin's Minute (as in small) Waltz.
It's always called Chopin's Minute (as in 60 seconds)
Waltz.
Remember Hinge & Brackett? Funny as they were, they were very able musicians, and I remember an occasion when Dr Hinge attempted to play the Minute Waltz in under a minute. He/she did it, but at a ridiculously fast speed. I think he/she said then that it's probably so titled because it's quite a short piece in comparison with many waltzes of the period.
It's a bit like a 'ten-minute' recipe or makeover - it often takes longer than the title would suggest.