Minimum design for controlling 2 LEDs to light either one or both?
No. Without adding extra components (Diodes) you can not use SPST buttons.







simulate this circuit &ndash; Schematic created using CircuitLab

If you use a DPST or DPDT switch instead, quite easy to find, you can avoid the diodes. You would ignore the extra pins on the DPDT switch.







simulate this circuit