I think the code below will do what you want (semi-tested). But I'd have to booster pretty strongly against the perl solution. In this case you probably should do it with CSS. If the blockquote is truly a "quote," okay, but if you're only changing it for the formatting, you should format from without. Both solutions are below.

use strict;
use HTML::TokeParser;
use CGI qw( blockquote );

my $string = join '', <DATA>;

my $string_ref = \$string;

my $p = HTML::TokeParser->new( $string_ref );

my $html;
my $last_end_tag;
while ( my $token = $p->get_token )
{
    if ( $token->[0] =~ /[TCD]/ )
    {
        $html .= $token->[1];
    }
    elsif ( $token->[0] eq 'S' )
    {
        if ( $token->[1] eq 'p' and $last_end_tag eq 'h4' )
        {
            $html .= blockquote( $token->[2],
                                 $p->get_text('/p')
                                 );
            $p->get_token(); # toss the </p>
            $last_end_tag = 'blockquote';
        }
        else
        {
            $html .= $token->[-1];
        }
    }
    elsif ( $token->[0] eq 'E' )
    {
        # if it's a new blockquote, it's closed already
        $html .= $token->[-1]
            unless $token->[1] eq '/p' and $last_end_tag eq 'h4';

        $last_end_tag = $token->[1];
    }
}

print $html;

__END__
<p>Stand alone p, or, aw, skip it.</p>
<h4 class="title">This is an h4</h4>
<p class="salad" id="taco">A first paragraph.</p>
<p>A follower.</p>
<p>Big finish. Or Finnish?</p>
[download]

CSS solution.

blockquote {
 /* format definition, whatever you want... */
 margin:1em 1em 1em 2em;
 font-style:italic;
 font-size:105%;
}
h4 + p {
 /* format definition identical to your blockquote def */
}
[download]

update: fixed grammar flatulence + one more, sigh.