Hey there,
I understood about a device not having an earth connection being safe, but my concern was that I wasn't sure if my SMPS had an earth connection or not, since it was plugged into a power strip that did have an earth connection.
In doing more research and asking on Reddit as well, I've learned that if the power supply has the double square symbol on its label, it means it's a Class II double insulated supply using flyback technology, and is mains earth isolated. Also, the SMPS having two prongs with no ground pin is not sufficient to determine that it is isolated (although the vast majority of the time it is) -- in North America the neutral conductor of the wall outlet is connected to mains earth at the breaker panel. So you would still be connected to earth ground if this symbol wasn't on the device.
Thanks!