I guess it depends on your internet connection. I had assumed you would be travelling about, not in an apartment....
WiFi security is too easily hacked. Every year or so they announce a new standard of security, that is unbreakable. Few months later it's hacked. I don't know the current status... but if it's not yet hacked, past experience is that it will be soon.
If you are using public access computers, well too many opportunities for key-loggers. If you are at home, or at a hotel, and using a wired connection then I would feel safer. But do recall that in China they are actively and openly monitoring all internet traffic. Though, obviously your banking info is not #1 on their list of interesting-things-to-look-at if your balance is small enough that you want to save the $2 ATM fees
It's not that I
think that your online banking info will be hacked, it's just that if it is, can you imagine getting it sorted out, while keeping your living funds flowing, if the account is in the US and your accessing it in China.
But I'm really really conservative with where I will do my online banking. And I'm not a Luddite... I use my cc all the time to pay for things online, or pay bills online, or transfer money online. It's not the online-ness that worries me... it's the connection from my computer to the bank that worries me. If you are confident that that bit is secure, then bank away I say!
PS HSBC = Hong Kong Shanghai Banking Corp, iirc, though they changed their name when Hong Kong changed status, I think, and I think they have their HQ in Hong Kong or London. But they are big and global.