The short answer is Shakush Al-Kafer (Sha-KUSH Al-KAAfer) is "Hammer of the Infidel"

The long answer is that, you're pretty right on as far as your research. There are a couple of ways to say it. There is a formal, official Arabic and there is the Arabic that people use to talk to each other. The latter one changes quite a bit depending on where you go, but luckily the words you use don't change too much.

In the spoken Arabic, the work is Shakush, Shakuch (both Egyptian), Chakuch (Iraqi). Infidel is the same; Kafer.

Therefore Shakush Al-Kafer would be the words you would probably want to use.
Sha-kUsh Al-KAA-fer. The "a" in Kafer is stressed, the "u" in Shakush.
Sometimes when people are speaking fast, they cut off letters. It happens in English and Spanish. This is why you sometimes get something like Shakush 'l-Kafer.

Official Arabic the word for "hammer" is Matraqa.
Infidel is Kafer.
Hammer of the Infidel would be Matraqat Al-Kafer
The "t" at the end is a grammatical addition.

The "e" and "i" in Kafer (Kafir) are more or less according to preference, The A" is not. Nor are the vowels in Shakush changeable.

Lion of Cairo would be Asid Al-Qahira
Asid (Ah-Sid)(like the English word "Acid"). Cairo is called Al-Qahira in Arabic. Al-QAA-hi-rah (the "i" is like "hit"). The stress in Asid is on the "a" and in Al-Qahira on the "a" following the "q".

Banish is a word that a lot of uneducated Arabs probably won't understand. To say "I banish you" would be Amheeka (if speaking to a male) or Amheeki (if speaking to a female). Saying Amheek without the "a" or "i" is not perfectly grammatically correct but would be much more widely used, since it's easier.

Hope this wasn't too confusing.

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