my @sorted = qw(
    02_org_name
    03_org_addr1
    03_org_addr2
    04_org_city
    ...
);
my %swip_data;
@swip_data{@sorted} = map {
    defined $cgi->param($_) and $cgi->param($_)
       or print "You must define a $_.<br>" and ''
} @sorted;
[download]

<update>... you are printing the form fields first:

my @sorted = qw(
    02_org_name
    03_org_addr1
    03_org_addr2
    04_org_city
    ...
);
my %swip_data;
my @missing;

@swip_data{@sorted} = map {
    print "$_ :" . $cgi->textfield(-name => "$_") . "<br>";
    defined $cgi->param($_) and $cgi->param($_)
       or push @missing, $_ and '';
} @sorted;

@missing and print "You must define these fields: ",join(', ', @missin
+g),".<br>\n";
[download]

No need for double quotes here:

    if (defined $cgi->param("$_")) {
[download]

and no need for explicit concatenation here:

    print "You must define a $_." . "<br>";

    print "You must define a $_.<br>";  # less noise
[download]

Unless you use $arin_tmpl elsewhere, just say

print <<END_TMPL;
[download]

If you populate the array first, and from there your hash, you don't need n_ to maintain order.

</update>

--shmem

_($_=" "x(1<<5)."?\n".q·/)Oo.  G°\        /
                              /\_¯/(q    /
----------------------------  \__(m.====·.(_("always off the crowd"))."·
");sub _{s./.($e="'Itrs `mnsgdq Gdbj O`qkdq")=~y/"-y/#-z/;$e.e && print}