TPS63001 to power arduino

If you were looking for +/- 1 bit accuracy from an ADC powered by this switcher without any filtering, IMO you 'might' have an issue.
@ 10 mV noise the split is +/- 5 mV. with a little filtering provided by the board and some small oversampling, I don't think there is any issue at all.
even with the 1V1 ref on an Uno or 2V56 aref configured on a mega. a 100 uHy choke and a 47uF cap as an input filter and a 22uF cap as output filter you should be fine
at 50KHz a 100 uHy choke has about 3k ohms of reactance at 150 KHz it is 3 X that with a dc resistance of under an ohm a switcher inductor of that value is perfect
in that the magnetics are shielded, there's no radiation from the choke and no need to shield anything... IMO and in the case of several prototypes I built with small
Linear tech LT1172 switchers never an issue.

Doc

{I neglected to mention that I removed the filtering (3 1206 parts) in production as they weren't required at all... Edit}