Ahh I had my units wrong. So it looks like a TPIC6B595 will satisfy my requirements.
What about a shift in register ? Is it better to daisy chain multiple parallel to serial shift registers and read via SPI ( for my 34 buttons ) or go for an MCP23xxxx over I2C or SPI and then get interrupt capability ? I suppose the question is, with a 180Mhz Teensy 3.6 reading he shift registers for input would I need to worry about interrupts ?