Upgrade cheap power supply
You can further smooth the output by increasing the output capacitance, but to power a MCU or RF transceiver I would use an LDO or buck converter(if efficiency is important) .

Your voltage will have to come down slightly but your chip will most likely run from 4V fine if you were able to run them with 5. 

Your RF chip will probably have an input ripple requirement that will need to be taken into account when selecting an LDO along with peak current requirement.