I didn't see this on the frequently-asked-for thread or in the first several posts, so I'm hoping this is not a tired suggestion.
What I'd like to suggest is an "off switch" that can be applied to individual pets. When toggled, those pets would not show up in the drop down list at the Ultimate Pet Zapper. Optionally, this could be extended to potions and elixirs as well - these pets would not show up in the list for those items.
This off switch could be toggled back and forth at any time.
Accidentally morphing or zapping a pet happens to all of us, I'm sure, and Subeta is very gracious in allowing us to reverse a mistake one time. But it's something that I live in fear of doing all the time. Okay, live in fear is a bit melodramatic, but I would be very unhappy if I was to change the wrong pet. Every time I visit the zapper, Anozira shows up first because she's my first listed pet, but I always feel a little heart flutter of concern to be extra careful to choose the right pet, because I would be quite upset if she or her minion were to be changed.
The default to this switch would be on - pets would automatically show up in the zapper and potion/elixir lists, and users would have to opt out certain pets. That way the pet could be turned "off" only when their owner was satisfied with their "final" form.
It'd also make it easier for us users with a plethora of pets to keep track of the ones we are zapping instead of having to sift through all of the pets.
Support--I remember instances where the content on the page would skip down a little, which can lead to accidentally selecting the wrong pet. I think that's been fixed for the most part, but anything from lag to faulty touchpads could cause an expensive and frustrating accident. I definitely wouldn't want my experiment pets to get zapped after already zapping them for a long time.