The problem was that although the hotel chain had already been established in Singapore in the early 70's, it had yet to open anywhere in Hong Kong. This ruled out the location being part of the proper hotel chain itself but gave no clues as to what the place was. Anyway, after a long wait for more information to appear, it turns out that there was indeed a Club Shangri-La and its sign can be seen in HT Wong's picture of Hankow Road in Tsim Sha Tsui right here.
This is the part of Hankow Road that is to the north of Peking Road. Peking Road is the bit at the bottom of the frame. Pretty much all of the visible buildings in that picture have been redeveloped, but it looks as though the club was located in the basement of the precursor to the Hong Kong Pacific Centre.
I think some of gweilo8888's observations from his research are worth preserving because it's quite possible one of the companies he mentioned in his original comments were behind the club. Here's what he had to say:
...Clearly from the identical font, if there *was* a bar / club / lounge of some kind before the hotel, it would have to be run by a related company. Although the hotel didn't exist as far back as the 1970s, related companies not surprisingly did. (They'd have had to exist in some form before design and construction of the hotel property started, of course.)
The earliest record I could find in the companies registry was for Shangri-La Hotel (Hong Kong) Limited aka 香格里拉酒店[香港]有限公司 (15-Aug-1972). The company itself still exists, but as of 04-Jun-1996 it had become Auto Plaza Limited. That's probably our best candidate.
Our second-best choice would be Shangri-La Trading Limited aka 香格里拉貿易有限公司 (19-Apr-1974). They never changed name, so I can't definitively connect them to the hotel group -- it could just be a coincidentally-similar name -- and they've long since ceased business.
Anyway, here are the screen grabs.
That's Ho Pak-kwong as the doorman
It's also possible that the company responsible for this club was using the hotel name in a blatant case of trademark infringement. If so, then once the hotel was made aware I am sure the club changed name or closed down. If anyone remembers it, please feel free to chime in.