Need advice on new device regulatory requirements
You can't tag if you didn't test...

You cannot claim your device is approved by those standards bodies if you have not sought approval from them. The fact that your power supply is certified means that you will face much less difficulty getting your device approved (all of the AC standards have already been met and tested for you, yay!), but your device is not necessarily compliant with other relevant standards just because you used a good power supply. 

There's more to certification than just the AC/DC power supply...

Depending on what your device actually does (medical, industrial, consumer) and what devices it actually contains (motors, electrodes, etc) and what voltages are present during operation and after power is disconnected, you will have to comply with relevant standards. Another set of standards to worry about concerns unintentional radiation (regulated by the FCC in the US and others worldwide). 

So simple put, Power supply certification is insufficient to claim compliance and if you do so, you will be violating those laboratories trademarks and can be held liable for those damages.