Effect of switching noise on a handheld measurement device
I think that Cypress have invested a fair amount of money in developing this chip and the first thing i'd do is try and get reassurance from them about your concerns. Obvious (or not) PCB layout will be key to avoiding noise problems on your analogue circuits so follow the guidelines they give on PSU layouts in the PDF.

From my standpoint, I've recently developed a circuit that has 16 strain gauge inputs, provides DC constant current bias for them, amplifes and filters them, converts to digital, combines the ADC streams and applies "comms" header to give a single 500kbps serial stream and transmits it to a receiver via a local FM transmitter. It also has a switching regulator on board and I know there is no noise I can measure that is attributable to it.

This design has good low noise performance (2mVp-p is typical input signal) and the noise performance would have been a lot worse should we not have used good PCB layout practises.

It boils down to: -

1) Do you trust a reputable chip supplier to sell a device that is compromized

2) Why not seek assurances

3) Circuits that require much higher noise performance work with SMPSUs

4) Layout, good layout.