Should I get a full desk mat that overhangs on a small desk?

Yes, a full mat that overhangs slightly (1-2cm) is better than a smaller pad because it prevents your forearms from resting on the raw desk edge or sharp front, which gets uncomfortable fast. Most mats are thin enough that the overhang won’t curl or get in the way, but avoid more than 3-4cm of overhang or it will slide around. Your wrists will thank you.