I don't think Japanese people are sensitive to being called Jap, are they? To me, it's like us being offended being called Brits...
Even the word Paki wouldn't be a "thing" if it wasn't made to be. I'm from Bradford - and when I was a kid the Pakistani shopkeepers used to laugh and say "you'll always have a Paki shop on Christmas Day if you need owt!"
It was only when idiots used it as an insult it became a "horror word" :0(
A word isn't just a word though. It's all about the historical use and the meaning that it then takes on.
No group of people has ever used Brits as derogatory. The words that you are saying "aren't that bad" hold a slanderous meaning due to their historical use as derogatory terms and are therefore offensive.
Would it really hurt to smash the keyboard a few more times and write 'The Japanese' or 'Pakistanis'?