Design of a switchable dual voltage power supply
To reduce ripple and peak current, at the expense of reduced voltage, you can add an inductor to the positive and negative legs to make a choke-input filter. This will also reduce the chance of destroying the diodes from the inrush current on closing the switch.

The chokes can be optimized to reduce ripple, in which case output would be closer to RMS than peak voltage, or a smaller choke would increase the output and ripple, yet might keep peak current tolerable.

Incidentally, choke-input filters reduce transformer heating because of lower peak current, so average power output does not suffer, though the output voltage is less.