No hh45, the four year immunity period applies to both building operations and to changes of use of existing structures to use as a single dwelling house.
Ten years for everything else.
Since the erection of the outbuilding constitutes ‘building operations’ the four year period applies (in principle, and subject to the “deliberate concealment” point).
The planners will not “waive through anything” (given that we have no information from the OP as to any restrictive planning designations that might apply – for example green belt, AONB, conservation area, proximity of listed buildings or any one of many other restrictions) so I think it’s a little unwise for the OP to just go ahead.
As onzadog has correctly identified already, an indemnity won’t prevent enforcement action if the local authority are minded to enforce and the presence of the outbuilding appears to be the making of this particular property.
‘Get an indemnity and go for it’ is (in my view) not an appropriate course of action.