How to turn an SPST momentary push button into a momentary DPDT?
simulate this circuit &ndash; Schematic created using CircuitLab

Figure 1. Use a relay to provide DPDT action from a single push-to-make pushbutton.

The relay coil voltage should be the same as the supply, V+.

The contacts should be rated for > switching voltage and > switching current. In your case it is small signal so it may be more important to get gold-plated contacts which won't corrode and degrade the small signals.