Renewal of residence permit

I need to renew my residence permit - I live and work in Ningbo and have another part-time job in HK. I have been informed that it will take 15 working days to renew my residence permit. This will adversely affect my job in HK which I travel to weekly. I understand that a letter is available from the relevant authorities confirming that the passport is held by them thereby enabling the person to travel within China without their passport. Can I obtain such a letter thereby allowing me to travel to HK for my job? Or can they renew the passport in less than 15 days?