How do I boast only in Christ when applying for a job?

I think there's an external boast and an internal boast.

Internally, as you offer yourself with your skills—and that's what they're getting at: you have to sell yourself to get a job—you are saying,

"God, if I have any skills this company needs from me at all, they're from you. And I thank you."

"I thank you that I know video stuff," or "I thank you that I am really fast as a typist," or "I thank you that I have learned engineering skills."

"And this is a gift from you, and I just want to speak the truth. I don't want to overstate the case about what I'm capable of doing or understate the case of what I'm capable of doing. I want to just tell the truth, and inside I'm thanking you and I'm humbly submitting to you as my benefactor and my lord."

Now the external, verbal part—if you sense it's appropriate (and I think it would be, usually)—is to say who you are, what you can do, and just say "I'm thankful to God that he's let me get an education in engineering," or whatever field it is.