From the materials listed, this sounds a lot like how it works at the Post Office (JP Bank). Simply for reference, this is how it worked for me:
1. I found the pamphlet for Remittance and flipped to the English section.
2. I found the proper form for what I needed.
3. I took all of those supplies to the bank.
4. I pointed at the form I needed in the pamphlet.
5. The form is bilingual, so I filled out it. Be sure you have the swift/ban code or routing number (which is possibly U.S. only), branch, bank address, account number, your address, your telephone number, the receiver's name, and the receiver's address.
6. Hand over the completed form with your zairyuu card and bank passbook for verification. I think I also might have given them my Health Insurance card and foreign ID my first time. They might request your hanko seal as well, although I didn't need it for that trip.
7. I sat down for an extended period of time as they figured out the process, and I fixed a few mistakes I had made.
8. They printed off the official exchange rate, I told them how much I wanted to send, they confirmed the exchange and reminded me of the transfer fee.
9. A little more waiting and I was done.
It took maybe an hour, could have been quicker if we weren't flipping through dictionaries half the time. If you need to get it done stat and you don't have a translator available if you feel like you need one (I'm sorry, I've forgotten what your level is), then I would say just go ahead and try. The paperwork is probably multilingual and there's not that much essential discussion to take place.
Mind you, it took my transfer 2-3 weeks to process. For your first go you might face similar waiting times.