The Hugo statistics are up as a PDF and linked to from here, and with comparison from the Puppy slates which are linked to from here, it's possible to extrapolate what the Puppy-free ballot would have been.
I'm not sure if anyone else has already done it, but I'm awake and at home and don't have parties to attend, so here are hypotheticals for the four fiction categories and Related Work, all of which were particularly disfigured by puppydom and for which I can be fairly confident that none of the Puppy candidates would have made the ballot without the slates' help. (A judgment that cannot be made for the Best Editor categories, let alone the Best Dramatic Presentation ones.)
Key. A = made the real ballot anyway despite the Puppies' help. B = made the ballot due to the ineligibility or withdrawal of Puppies. Note: There are typos and errors on the statistics (e.g. "Katherine Anderson" for Addison), and I may not have caught others.
Ancillary Sword, Ann Leckie (A)
The Goblin Emperor, Katherine Addison (B)
The Three Body Problem, Cixin Liu (B)
Lock In, John Scalzi
City of Stairs, Robert Jackson Bennett
"The Slow Regard of Silent Things", Patrick Rothfuss
"The Regular", Ken Liu
"Yesterday's Kin", Nancy Kress
"Grand Jete (The Great Leap)", Rachel Swirsky
"The Mothers of Voorhisville", Mary Rickert
"The Day the World Turned Upside Down", Thomas Olde Heuvelt (B)
"Each to Each", Seanan McGuire
"The Devil in America", Kai Ashante Wilson
"The Litany of Earth", Ruthanna Emrys
"The Magician and Laplace's Demon", Tom Crosshill
BEST SHORT STORY
"Jackalope Wives", Ursula Vernon
"The Breath of War", Aliette de Bodard
"The Truth About Owls", Amal El-Mohtar
"When It Ends, He Catches Her", Eugie Foster
"A Kiss With Teeth", Max Gladstone
BEST RELATED WORK
What Makes This Book So Great, Jo Walton
Chicks Dig Gaming, Jennifer Brozek et al
Shadows Beneath: The Writing Excuses Anthology, Brandon Sanderson et al
Invisible: Personal Essays on Representation in SF, Jim C. Hines
Tropes vs. Women: Women as Background Decoration, Anita Sarkeesian
One thing to note is that vol. 2 of Bill Patterson's Heinlein biography still wouldn't have made the ballot; it's 6th place on the Puppy-free list.
Another and most important thing to note is what this does to the male-female ratio of authors in the fiction categories, a topic of which I've written before. The actual ballot had 17 stories by men and 3 by women (15% women). The Puppy slates, taken as an aggregate, had 20 stories by men and 3 by women (13% women). The Puppy-free ballot above has 9 stories by men and 11 by women (55% women), which is in keeping with the post-Racefail numbers of recent years' Hugo nominees, and puts the lie to the Puppies' claim that they're increasing diversity, at least on this axis.