I'm a citizen of Uzbekistan holding stay permit in China , can I apply for Z visa in HongKong

I was working in Qinzhou city as an English teacher. I came to Chengdu to work, with release letter from previous school. But, enter exit beaurou changed my residence permit into stay permit for one month in Qinzhou. CD enter-exit beaurou says they can't change it to residence permit, they are asking me to prosses Z visa in HongKong . So, can Uzbekistan citizen go to Hong Kong to obtain Z visa? If not, which country can I go to obtain it beside my homecountry and HK? Thanks.