A join is the right thing to use. Your grep/map thing looks bad because you're trying to do too much at once.

sub with_no_map {
    my @lines;
    while <DATA> {
        chomp;                # removes trailing newline
        next unless /\S/;     # skips blank lines
        @values = split /;/;  # gets individual records
        @values = map {quotrim($_)} @values; # quote vals

        # normalize number of values by padding with NULL
        if (scalar(@values) == 3) {
            splice(@values, 2, 0, 'NULL');
        }
        my $values_group = '(NULL, ' .
          join(',', @values) . ')';
        push @lines, $values_group;
    }
    return join(",\n", @lines);
}
[download]

Untested, but hopefully you get the gist.