I'll just add that CGI::Application's source is short and simple - it should be easy for anyone to alter it to taste if that's really nessessary. It so happens that C::A is nicely OO so you frequently get the custom behaviour you want by overriding the appropriate methods. In my copy of C::A I don't even see $SIG{__DIE__} being tweaked directly at all - I'd just think that's from the use CGI::Carp near the top of the module. So... whatever new thing you needed it to do regarding $SIG{__DIE__} ought to be easily within your reach.

__SIG__
use B;
printf "You are here %08x\n", unpack "L!", unpack "P4", pack
  "L!", B::svref_2object(sub{})->OUTSIDE;
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