Two options for a circuit I am trying to construct. The DPDT switch allows simultaneous toggling between solid and blinking LED's in two separate fixtures powered by two separate C2032 cells. This much works.

I want to add an off switch that turns both off simultaneously. Due to size constraints, soldering in my spare DPDT switch will be difficult. If the two circuits share one SPST switch, will this work safely? Or do I need to find a really tiny DPST switch to make this work?