Spent a few hours last night making a list of pets I would definitely use my stones on. The pets in this list all only have 1 breed (with 1 or 2 genders) and cannot be caught in the wild (meaning no chance to get a blue, unless u upgrade with a stone).
As you can see, beasts have the most pets to upgrade. I would say it's safe to use flawless stones on beasts.
Aquatic
Wood Frog
Tree Frog
Jubling
Speedy
Mr. Chilly
Sea Pony
Tiny Goldfish
Fishy
Beast
Bombay Cat
Cornish Rex Cat
Black Tabby Cat
Orange Tabby Cat
Siamese Cat
Silver Tabby Cat
White Kitten
Albino Snake
Black Kingsnake
Brown Snake
Crimson Snake
Worg Pup
Smolderweb Hatchling
Cobra Hatchling
Baby Blizzard Bear
Dun Morogh Cub
Durotar Scorpion
Calico Cat
Darting Hatchling
Deviate Hatchling
Leaping Hatchling
Obsidian Hatchling
Ravasaur Hatchling
Razormaw Hatchling
Winterspring Cub
Feline Familiar
Critter
Winter Reindeer
Mr. Wiggles
Whiskers the Rat
Wolpertinger
Egbert
Peanut
Pint-Sized Pink Pachyderm
Spring Rabbit
Elwynn Lamb
Mulgore Hatchling
Perky Pug
Imperial Silkworm
Scooter the Snail
Dragonkin
Proto-Drake Whelp
Thundering Serpent Hatchling
Elemental
Tiny Snowman
Spirit of Summer
Teldrassil Sproutling
Ammen Vale Lashling
Withers
Sapphire Cub
Flying
Green Wing Macaw
Miniwing
Plump Turkey
Blue Mini Jouster
Gold Mini Jouster
Tiny Flamefly
Imperial Moth
Humanoid
Peddlefeet
Father Winter's Helper
Winter's Little Helper
Curious Oracle Hatchling
Curious Wolvar Pup
Magic
Willy
Enchanted Broom
Toxic Wasteling
Enchanted Lantern
Magic Lamp
Legs
Lunar Lantern
Festival Lantern
Gusting Grimoire
Mechanical
Mechanical Squirrel
Mechanical Chicken
Pet Bombling
Lil' Smoky
Lifelike Toad
Tranquil Mechanical Yeti
Clockwork Rocket Bot
Mechanopeep
Warbot
Personal World Destroyer
De-Weaponized Mechanical Companion
Mechanical Pandaren Dragonling
Undead
Sen'jin Fetish
Creepy Crate
What to definitely use your stones on
Re: What to definitely use your stones on
Already such a list among the stickies, look at the uncommon only list.