What's the smallest and lightest way to supply 5V to a 1"x1" circuit board?
Why don't you use a CMOS 555 that will operate happily from a 3V battery, even at the end of (battery) life? 

If you actually need 5V for blinky LEDs or whatever, you will need a circuit very similar to the ones you are showing.. so you could save mass by designing a very thin and small custom PCB. You can easily get 2-layer PCBs as thin as 0.4mm and you could probably cram that stuff into 1/3 or 1/4 the area, and use more compact components for the diode and the capacitor, so the total mass should go down by a large factor.  

For the ultimate in reduction, pick a very high frequency switching chip that has synchronous rectification, as as the FAN4860, which operates at 3MHz with a tiny 1uH inductor and tiny 0402 ceramic capacitors. The chip itself is 1.2mm x 0.88mm x 0.5mm, almost an inhalation risk. 



Here is a comparison of the chip size vs. the (relatively) massive SOT23-5 package used by the vendor you linked to: