Case analysis with REGEX

I have some data like

small_animal/Mouse
BigAnimal:Elephant
Not an animal.

What I want to get is:

Mouse
Elephant
Not an animal.

Thus, I need a regular expression that searches for / or : as follows: If one of these is found, take the text behind that character. If neither / nor : exists, take the whole string.

I tried a lot. For example this will work for mouse and elephant, but not for the third line:

(?<=:)[^:]*|(?<=/)[^/]*

And this will always give the full string ...

(?<=:)[^:]*|(?<=/)[^/]*|^.*$

My head is burning^^ Maybe, somebody can help? :) Thanks a lot!

EDIT:

@The fourth bird offered a nice solution for single characters. But what if I want to search for strings like

animal::Dog
Another123Cat
Not an animal.

How can I split on :: or 123?