You can explictly set $CGI::POST_MAX to some value in your instance script. You will need to pass the query object via the new() method so that it is inherited by your application module.
For example, your instance script may look like:

#!/usr/bin/perl -T

use strict;
use warnings;

use lib '/home/lib';
use Current::My_App;

use CGI;
$CGI::POST_MAX=102400; # Limit post to 100kB
$CGI::DISABLE_UPLOADS=0; # Allow file uploads
my $q=CGI->new; # Create query object
if ($q->cgi_error()) {
    print $q->header(-status=>$q->cgi_error());
    exit 0;
}

my $app=Current::My_App->new(query=>$q);
$My_App->run();
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As for determining the MIME type of a file, the File::Type module might be useful for your needs.