Available programs that can verify the working of a simple substitution cipher
Regarding the test of unicity

You could just script the test in Python (or any other language, really). The language in which you already implemented your cipher might be a good choice otherwise.

Then, given the size you are talking about (256 possibilities of 16bits = 4Ko), you can basically just generate all the results in a 256-array, and check the unicity of each element in your array.

Regarding your cipher

I've got a pretty hard time figuring the security level of your application. With a basic substitution over basically each character (8bit), your ciphertext is extremely vulnerable even with not-so-long messages, and especially if your data/protocol/application has any kind of predictable headers and such. It's not clear which kind of threat you want to protect the data from.