Travel Republic website offer Disney hotels as a room only option but whether they will for 1 night or not I'm not sure. Even if they did, the chances are you'd have to move rooms because I don't think Disney would be able to link your booking with them with your external booking, although I'm not 100% sure.
I totally understand why you don't want your arrival day to be your first day with Disney because it feels like such a waste. We always stay in another hotel outside of Disney on our arrival day so that we are ready to go early on the first official day. We stayed in the Magic Circus last time which was wonderful, we really enjoyed it, but it's a bit pricey, about £130 I think we paid. For our next trip we have booked into the F1 hotel in Meaux. It was about £40 for the night and there's plenty of places to eat nearby, it's on a retail park type thing so there's Pizza Hut and other places like that. Then we will go to our Disney hotel about 7.30am the next morning, get our park tickets and off we go!