You could cut yourself if you're not carefull, but if you do it the right way you don't risk that much.

The proper way to grab the blade of your sword, be it for half-swording as shown in the meme or to go for a mordslag, would be to put the bottom of your palm on the flat of the blade, and then wrap your fingers around the edge without touching, and holding the other side of the blade with just your fingertips. This way there is actually a space between the edge, and your hand.

You could even test this method with a kitchen knife if you want to. You'll be surprised by how actually stable this grip is.

Additionaly, even in case of "naked" combat, people often uses leather gloves which do in fact provide a fair bit of protection against accidental cuts.