This letter does represent this kind of sound, so you're correct. However, the strokes are not in correct order and break at wrong places. The correct order is as follows:

1. Write the ㄱ first, from top to bottom, in a single stroke, like a sideways J. The hook ending is obligatory;
   
2. Write the 丿 second, cutting the first stroke;
   
3. Add the 丶 on the right. If you stop at this point, you'll get か (ka);
   
4. Place the " over the letter to make it が (ga).
   

However, Japanese has two basic alphabets, hiragana and katakana. For things like foreign words and onomatopoeia, you should use katakana instead, as hiragana is used to write native words. Briefly saying, が is correct, but if you want to step it up, use ガ.

"but gors that's exactly the same thing but without the 丶 and the ending hook"

This is because both letters originate from the same source. All hiragana have their corresponding katakana. It's comparable to us having two different alphabets, one for UPPERCASE and another for lowercase.

If you want to attain grorious nihonjin desu ne status, add a small ッ (tsu) on the end. This letter means 'sudden pause' and it's perfect for this kind of sound. Use ガッ!

See "ガッ" in action here: