I bet you will find it is no problem in this market, I rented my first place without HK ID or visa. Generally most forms here have a place for ID number or alternately your passport number.
try W studios .. www.wstudios.com.hk
it's central , affordable, comfortable, nice people running it and flexible on how long you want to stay.
I am living there at the moment, and its very conveniently located.
cheers
AKD
I just recently rented a service apartments before getting my visa, service apartments are more flexible you can rent short terms, 1 months or more. You will need to put up a deposit.