I think it's safer to pass an argument.

Secondly, env $^X makes no sense. You want one of

• exec $^X, ...
• exec 'env', 'perl', ...
• exec '/mypath/perl/bin/perl', ...

Your other changes would indicate you want the last.

Thirdly, the changes to PERL5LIB look redundant with the paths built into the Perl you want to be running.

BEGIN {
    if (@ARGV && $ARGV[0] eq '--fixed') {
        shift(@ARGV);
    } else {
        $ENV{PATH} = join ':', '/mypath/perl/bin', $ENV{PATH};
        delete $ENV{PERL5LIB};
        exec '/mypath/perl/bin/perl', $0, '--fixed', @ARGV;
        die ...;
    }
}
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