Full pass voltage regulator at undervoltage

Hi,
I'm working on a hobby project and wants to make it 5V as well as 3.3V compatible. It has an Atmega328 Pand HC05 bluetooth module. What I want is the device to work whether I provide 5V or 3.3V. 3.3V or 5V doesn't matter for the MCU but for HC05 it does as it works at 3.3V. So I'm looking for a cheap voltage regulator which provides full pass functionality i.e the regulator should provide 5V to 3.3V regulation but if the voltage falls below the minimum dropout range (which happens when we provide 3.3V input), the regulator must be capable of passing the input to the output. I have seen such regulators, but looking for cheap ones you can easily source from eBay, alibaba etc.

Thanks.

This meets your requirement and would work with battery power. You have full specifications here. Anything cheaper may not be fully or correctly specified and product quality and reliability might be an issue.

Pololu 3.3V Step-Up Voltage Regulator U1V10F3
Pololu 3.3V Step-Up Voltage Regulator U1V11F3 (with shutdown option)