Although I normally don't like editing XML files with anything other than a proper module, in this case it might be appropriate. Also, luckily, the <?xml...?> declaration happens right at the top of the file. The following will work if the only change you are making is "utf-16" to "utf-8", obviously it won't work if the name of the target encoding is longer...

open my $fh, '+<:utf8', 'file.in.xml' or die $!;
my $line = <$fh>;
$line=~s/<\?xml.+encoding="\Kutf-16"/utf-8" /
    or die "didn't match line: '$line'";
seek $fh,0,0 or die $!;
print $fh $line;
close $fh;
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