Hi silent_pain
I could be completely wrong here, and then maybe not, but 'wellies' is short for Wellingtons/Wellington boots, which are boots that people wear in the rain or when it's muddy out.
"get hitch" means to get married, which is viewed as a formal occasion as you know. So the fact that someone is wearing informal footwear to a formal occasion is interesting, to say the least. Kind of cool, actually, if you ask me.
