The simplest is to do {{mycard|core}}, but note that:
1. this will not wrap the card with any html tags, so you can't double click to edit, and
2. if there are any block (non-inline) tags inside the content itself, this won't fix them. Many basic cards, for example, have
tags inside their content.
If #2 is a problem there's not really an easy way to fix that, short of custom CSS to override the style rules. The one exception is on very short content, where you may be able to use {{mycard| closed_content}}, which will treat the content like the (shortened) content portion of a closed card.
#1 has some alternatives, however can often be fixed using {{mycard | display: inline}}, which will set the CSS directly on the element itself.
#1 is what I was looking for, mainly that css override. Now to modify all cards, I'd have to put it in the global CSS of the current skin no?