Skype numbers can not receive SMS messages - though it does have a service that allows you to send SMS messages. I don't think it is a technical problem that can't be solved - it is deliberate.
So yes, you still need a mobile phone number - if you need sms authentication.
You are going need one for potential emergencies.
Is there such as thing as a data only sim card in Hong Kong, and is it any cheaper or better than a normal sim with voice/data? I know in Japan this is possible and there are benefits to a data only sim with no number, but I did not think such a thing existed in HK.