I've shipped design samples to both Singapore and Australia, and in my experience, neither required a CE mark for the kind of items I was sending. Like others said, the CE mark is more for products going into the EU, so I wouldn't stress too much about it with Singapore or Australia unless you have something really unique or high risk. Always check the exact rules for your product though, because each country can be strange about certain electronics or materials. If you do end up needing to ship anything big, like a vehicle or something valuable, you might want to check out all the international transport options listed here:
https://www.a1autotransport.com/services/. They cover a huge range and usually give advice about documentation for different destinations.