Quite frankly, I think you're looking for something that doesn't exist. There are plenty of old kopitiams in Singapore, but they don't do dim sum on trolleys. Old school Singapore kopitiam food is all Peranakan, Malay, Teochew, Hakka etc; Cantonese people, and hence Cantonese food, are a distinct minority. While there are a few dim sum stalls, every one I know of expects that the customer walks up and orders what they want. Singapore being Singapore, I wouldn't be surprised if pushing trolleys around a shared space is a violation of their food license terms.