First, talking about wayang kulit and according to Infopedia:
One of Singapore's last Dalangs (dhalang in Javanese means puppeteer) was Wak Taslim Harjosanajo who passed away in 1985. Does it mean that wayang kulit had disappeared from the Singapore scene for 25 years?! I tried searching for more information on Wak Taslim Harjosanajo on the web but to no avail. A little disappointing indeed but I will try to fill this blank when I come across any related information.
As for whether Chinese shadow puppet ever exist in Singapore, I am afraid I do not have a definite answer for now.
Shadow puppet, Messenger from Hell dating from the 19th Century
Picture taken from Asian Theatre Puppets: creativity, culture and craftsmanship (from the collection of Paul Lin)