If you're getting into ducks, Storey's Guide (by Dave Holderread) is absolutely the resource to have. He has an entire chapter on butchering, including ages, how to do it, how to raise the birds for that purpose, and so on. Very very helpful.
Here is his paragraph on age:
"Depending on the breed and management, ducklings are normally in full feather for only 5 to 10 days sometime between the age of 7 to 10 weeks, except Muscovies, which require 14 to 16 weeks to feather out. Shortly after achieving full feather, young ducks go into a molt and begin replacing their juvenile garb with adult plumage. If ducklings are not dressed before this molt commences, butchering is best delayed for 6 to 10 weeks when their adult plumage will have been acquired." (Holderread, page 227)
That would put the *second* butchering age at between 13 and 20 weeks, whenever they complete their molt; or they can be butchered between 7 and 10 weeks if you catch them before the molt.
Enjoy. I wish I had the heart to butcher--duck is yummy--but I can't stand to eat those sweet little guys. I love them so much, even the drakes that I have too many of!