What is actually stored in your files? The literal text you provided in the string, or something else? If it is the text in the string then you can:

use strict;
use warnings;
use Encode;

binmode STDOUT, ':utf8';

print "Content-Type:text/html; charset=utf-8\n";
print "Content-Language: utf8;\n\n";

my $asText = do {local $/; <DATA>};

$asText =~ s!\\x(..)!chr(hex($1))!ge;

my $uCode;
my $newcode = decode('utf8', $asText);

print "<p>$newcode</p>\n";

__DATA__
\xc3\xa4    <span class="sy">\xc3\xa4</span>,
<span class="sy">\xc3\x84</span>
<span class="posg pos">Substantiv, Neutrum, das</span>
<span class="vg v"> \xc3\x84  \xc9\x9b\xcb\x90 das \xc3\xa4; Genitiv: 
+des \xc3\xa4 (umgangssprachlich: -s), \xc3\xa4 (umgangssprachlich: -s
+) </span>
[download]

Prints:

Content-Type:text/html; charset=utf-8
Content-Language: utf8;

<p>ä    <span class="sy">ä</span>,
<span class="sy">Ä</span>
<span class="posg pos">Substantiv, Neutrum, das</span>
<span class="vg v"> Ä  &#603;&#720; das ä; Genitiv: des ä (umgangsspra
+chlich: -s), ä (umgangssprachlich: -s) </span>
</p>
[download]