Strip from or something better?

Manipulating HTML with regular expressions is not a good idea. I suggest you use DOMDocument:

// input
$html = apply_filters('the_content', get_the_content());

$dom = new \DomDocument();
$dom->loadHtml($html);

$blockquotes = $dom->getElementsByTagName('blockquote');
foreach($blockquotes as $blockquote){
  foreach($blockquote->childNodes as $e){
    if($e->nodeName === 'p'){
      // create a text node with the contents of the <p>
      $blockquote->insertBefore($dom->createTextNode($e->textContent), $e);

      // remove <p>
      $blockquote->removeChild($e);
    }
  }
} 

// remove doctype
$dom->removeChild($dom->firstChild);            
$dom->replaceChild($dom->firstChild->firstChild->firstChild, $dom->firstChild);  

print $dom->saveHtml();