If you work with BerkeleyDB::Btree objects, I think you should subclass that, not BerkeleyDB itself. Then you'd write something along these lines:

package Myapp::BerkeleyDB
use warnings;
use strict;
use BerkeleyDB;
use base 'BerkeleyDB::Btree';

sub connect {
   my ($class, $dbname) = @_
   return $class->SUPER::new(
       -Filename => $dbname,
       ...
   )
}
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But note that I'm not familiar with BerkeleyDB, and the code is not tested.