Personally, I'd just get them something off their registry and leave it at that. I might get a smaller housewarming gift as well, if I felt like it. If I was only buying one gift, it'd be a wedding gift.
I'd also call it a wedding. I know some people have strong feelings about whether or not it's a wedding if it's not at the same time as doing the legal paperwork, but I don't at all. Sometimes you have to do paperwork at a different time. Your wedding is separate from that, in my opinion. Maybe that's because we had to get legally married the day before our wedding because it was a same-sex union.
I'd feel differently if they'd had a small wedding, followed by a bigger wedding. However, taking care of paperwork with the minimum of accompanying 'fuss' isn't your wedding, unless you want it to be. I didn't feel like the day that I signed my civil partnership papers was my wedding day. My wedding day was my wedding day.