The only problem I could think of here are the non-alphabetic characters. Some of them are not present anywhere else.

This should be taken care of by the conversion table that is available for you to use. But in some cases it is missing a handle. E.g. in Java, most solutions use MorseCode map even though it is neither named in description, nor imported or used in any other way in the initial code.

Hihi ^^

Everything is spelled correctly, as far as I can see.

Yeah, it starts with something that can be seen as garbage letters, but it is not.
In fact, you can look up those 'garbage letters' in Wikipedia. :)