Can a linear regulator in shutdown mode have the output in parallel with a switching regulator
Here is a low power LDO voltage regulator (TPS79733) that consumes less than 2uA quiescent current whilst delivering up to 10mA to keep your MCU ticking over when it's asleep. 

It has a fixed output of 3.3V and I think the clincher would be to arrange for your TPS63061 switcher to generate maybe 50mV more output (3.35V) so that when it gets activated, it sources all the higher current when you are taking 400mA.

In effect the LDO would not source any current because it would see an output voltage across its terminals that forces it to "open circuit" its pass-transistor.

Thus you don't need to enable/disable the LDO regulator.


  My question is how to handle this switch-over phase. The LDOs which I
  looked at have reverse current protection and may be put into
  standby/shutdown mode. Is this sufficient to not destroy the LDO when
  the switcher starts working?


Handling the switch-over phase - enable the switcher when the MCU powers up
Standby/shutdown for LDO protecting the LDO - the LDO will always be enabled.