Problem with mixed CMOS op-amp supply voltages on a square to saw wave converter
You can run the 4000 series parts off a bipolar supply but the voltage is limited (IIRC the limit is 20V total which works out to &plusmn;10V) and you need to level shift the input signal, this is perfectly doable with a comparator and a few resistors but it's still an extra part.

Or you can use a modern part like the ADG1219. It's a 2:1 mux rather than a plain switch so you don't need an inverter and it has a seperate pin for the logic ground so you can run it off a bipolar supply while controlling it with a unipolar signal.