I would like to use the word "know-how" in my letter of application. (I don't want to use "experience" as a replacement because I have used it before, therefore it wouldn't sound nice.)
Can I use it in this case or is it informal?
Use expertise, ability, skill, knowledge, facility, talent, command... if you don't want the (definitely) informal connotations of the somewhat childish...
know-how noun (informal)
1: ingenuity, aptitude, or skill; knack
2: commercial and saleable knowledge of how to do a particular thing; experience