Parents don’t want me to travel Watch
Also I would say a 3 week holiday isn't worth losing your family over, but then again it's also not worth kicking your kid out because they've gone away... Is that actually likely to happen or are your parents exaggerating and trying to guilt trip you into staying?
Having been to both Tokyo and Seoul, I felt a lot safer there than in some cities I've been to in Europe. You should show her the crime rates for these places, and just show her that they're both wonderful cities and are a lot safer than she probably thinks. Maybe just explain that you'll message/ring her everyday so she knows you're safe, and tell her what you're planning on doing each day, and hopefully she'll come around? Maybe even show her some pictures/vlogs as she'll see they're both a lot touristy and full of people...
Have you considered using something like a Starling (or monzo or whatever you prefer) account instead? Starling don't take commission so it doesn't cost extra to use, and if your wallet gets stolen or something, can just block the card on the app so it's not like you lose all the money like you would if carrying cash. I don't know if that's something that would suit you but it could be worth looking in to it, might make your parents feel better - less attractive to pickpockets if don't have wads of cash.
I'm a mum of an 18 year old daughter, so I do kind of get how they are feeling. If this was my daughter, I want to know everything. All the plans. I would also expect my daughter to be packing her suitcase herself at all times. And that she has a facility to wire money over to her should she need it. Id also need to see the person shes travelling with and if they are responsible, not reckless. You are 19, they cannot stop you from going, but if its first time travelling without parents, Id want to make sure my daughters done all her homework on her plans/cultures etc.