Hi there,
If you want to work in Hong Kong, you need to have a working VISA and to get a working VISA approved – you need a full time job to be sponsored.
In theory, yes you can get sponsorship for part time but you'll need to have a lot of projects and those projects must be able to sustain you a monthly income of a minimum of HK$20,000 per month so that you can survive in Hong Kong. Depending on the pay from the company, your schedule and willingness to work that would be quite difficult.
The main issues for a VISA sponsorship are;
1. Are you qualified and experienced to teach at any school, that way they can give you a lot of jobs.
2. You will need an approval from immigration
Good luck.