Being an extremely clueless newbie I wonder if the following approach will work for you.

#!
BEGIN { # Convert the warning to Carp::cluck
    $SIG{__WARN__} = sub {
        Carp::cluck(@_);
         };
     };
use Carp;
use strict;
use warnings;
use Mod1;
use Mod2;

INIT { # Clear the warning to Carp::cluck
    $SIG{__WARN__}='DEFAULT';
     };

sub One { # First definition
    return "first";
     };

sub One { # Second definition
    return "second";
     };

print One()."\n";
exit;
[download]

package Mod1;

use Exporter;
use strict;
use warnings;
@Mod1::ISA=qw(Exporter);
@Mod1::EXPORT=qw(One);

sub One {
    return "Mod1::One";
     };

    1;
[download]

package Mod2;

use strict;
use warnings;
use Mod1;

@Mod2::ISA=qw(Exporter);
@Mod2::EXPORT=qw(One);

sub One {
    return "Mod1::One";
     };
    1;
[download]

Running under Windows 2K/ActiveState 5.10 I get

C:\Code\SecCage>perl redef.pl
Subroutine One redefined at Mod2.pm line 10.
 at redef.pl line 5
        main::__ANON__('Subroutine One redefined at Mod2.pm line 10.\x
+{a}') called at Mod2.pm line 10
        require Mod2.pm called at redef.pl line 12
        main::BEGIN() called at Mod2.pm line 10
        eval {...} called at Mod2.pm line 10
Subroutine One redefined at redef.pl line 19.
 at redef.pl line 5
        main::__ANON__('Subroutine One redefined at redef.pl line 19.\
+x{a}') called at redef.pl line 19
Subroutine One redefined at redef.pl line 23.
 at redef.pl line 5
        main::__ANON__('Subroutine One redefined at redef.pl line 23.\
+x{a}') called at redef.pl line 23
second
[download]

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