I was trying to save you some trouble writing the server. Since that's already done, just use

my $response = $ua->post(
    'http://...',
    Content_Type => 'application/xml',
    Content      => $xml,
);
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Or if you need to twiddle with the request object,

use HTTP::Common::Request qw( POST );

my $request = POST(
    "http://...",
    Content_Type => 'application/xml',
    Content      => $xml,
);

my $response = $ua->request($request);
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sounds to me that it can not be handled by a form POST.

Of course you can't avoid using a form by using a form. I fail to see your point.