You could try dicing it up into about 1cm cubes and frying them up. Maybe just do a little bit first to see if your dog will eat them readily.
Kinda depends on which skirt you have as there are three all up. Two will pull apart fairly easily but one of them is a lot thicker than the others and should hold together better.
Skirt is a cut of meat that is usually used for casseroles etc as it's a tougher cut so if you cook it using a dry heat method (oven, grill, bbq, fryingpan) it should toughen it up for you.
If you think dogs can't count, try putting three dog biscuits in your pocket and then giving Fido only two of them. ~Phil Pastoret