Is it permissible to own a bag made 100% of crocodile skin?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.

The most predominant opinion of the Muslim scholars is that it is prohibited to eat crocodile meat because it is a wild animal that uses its fangs for catching prey.  The Prophet prevented us from eating fanged beasts as narrated by Al-Bukhari and others.  The crocodile is one of the amphibians and it is established that it can't be eaten.  Yet, scholars have different opinions about whether we can make use of the skin of animals that are forbidden, because some narrations indicated that it is lawful, while others forbade it.  One of the latter narrations is what was narrated by Abu Daawood and An-Nasaa'ee that Prophet Muhammad "Prohibited us from using the skin of wild animals (beasts)."  In another narration: "He prohibited us from using the skin of beasts and from riding them."

Abu Hurayrah reported as in the book of Abu Daawood that the Prophet said: "The angels don't accompany people who have the skin of a tiger with them."

The author of "Ar-Rawd Al-Murbi'", one of the Hanbali books, said that: 'We can't tan or use, after or before tanning, the skin of beasts such as the wolf or animals that are bigger than a cat and that are prohibited to be eaten.' 

So, it's not permissible to use the skin of the crocodile whether it was tanned or not because it is prohibited to eat it. 

This is the most predominant view and it also keeps you on the safe side, for the Prophet said: "Give up what you are suspicious of and adopt what you are sure of", narrated by An-Nasaa'ee and others.

Allaah Knows best.