Since HTTP::Tinyish is a wrapper over LWP, why not go with LWP directly?

my $browser = LWP::UserAgent->new();

my $header = HTTP::Headers->new(
                      Content_Type        => 'application/json',           
                      'api-key'=>"jhtty657");
                      #or maybe apikey=>"jhtty657" without the dash?

$url="https://somewhere.com";


$req = HTTP::Request->new( POST, $url, $header);
$req->content($data);

my $response=$browser->request($req);