All of the sound files are recorded by Advanced speakers only. Some of them may not be the best quality and some may be said in a relaxed rather than careful and clear manner.
The capital Q should be pronounced in an explosive manner from the back of the throat. It does sound a little like a q and H combined, but there should never be any closing of the front of the mouth that would make it sound like q and ch.
That's me saying HIQaH. I said it slowly so you could hear the Q sound. It should sound a little bit like someone who is coughing up something from their throat to avoid choking. I think you're hearing the onset of the Q sound, which means the first part of the word is exactly like HIq, and then you hear the rasping part, and are interpreting it as ch when it's actually a H sound. But if you are describing the sound "ch" as in Scottish "loch" or German "Ich" then you are hearing HIQaH exactly correctly. Meanwhile, Klingon ch is pronounced as in English "church."