use File::Basename;
# ...
# 4 elements at a time
while( my @cols= splice @files, 0, 4 ) {
  print Tr( {-align=>'center'},
    map {
      td( $_ ? submit(-name=>'file', -value=> basename($_)) : ' ' )
    } @cols[0..3]
  );
}

##</code><code>##

use File::Basename;
# ...
while( my @cols= splice @files, 0, 4 ) {
  print Tr( {-align=>'center'},
    td([
      map {
        $_ ? submit(-name=>'file', -value=> basename($_)) : '&nbsp;'
      } @cols[0..3]
    ])
  );
}