I agree with the above posters. You are far more likely to mess up the visa application than your new company, which has probably done this hundreds of times. Also as above, once you're in Japan you'll find that you don't know what's going on and aren't in control of the situation quite often, so maybe time to start getting used to that part of the culture shock
I came to Japan on a working visa 11 years ago, and my company sorted out my visa for me just fine. You'll still most likely have to visit the embassy/consulate at least once, so you'll be part of the process anyway.