Perk up = Feel better, became happier, more optimistic. Wrap up = finish, complete

Perk up = to feel better, regain energy, feel happier (in the short term). It implies recovering from a temporary bad mood or illness. I wouldn't use "perk up" in your example. > He drinks coffee to perk up in the mornings. > She was tired all morning but she perked up a bit after lunch. Wrap up = finish or complete something. You can say "wrap up writing (something) as in your example. > I have to wrap up writing my CV by next week when I apply for the new job. > The project is due in three weeks so we need to make sure everything is wrapped up in time.

I think you're using these words correctly. Here are your sentences with the grammar adjusted to sound better: "I perked up due to the improved situation in Japan these days." "I have to wrap up writing my CV by next week so I can apply for a new job."