I have been looking at a guitar (a Fender 70's Stratocaster) and I really like the look of it - the problem is that it has a U shaped neck and i have reasonably small, thin hands. Additionally, I also play with my thumb over the top of the neck. Would it be a big difference from the modern C neck guitar I am playing at the moment, and would it be too large for my hands?

I only know U-shapes from LTD guitars. The are kind of like a C-shape, but flatter on the back of the neck. For the thumb over the top of the neck playing I'd recommend something with a soft V-shape.
The Fender U-shape neck is meant to be like the second Telecaster necks, after they moved from the V-shape but before they went for the C-shape that became standard. They're very thick with high shoulders. Really good for standard rhythm playing because you've got one massive lump of wood in your hands that gives chords a lot of sustain and power but for fast playing it might be a little awkward for some people and it's hard to do thumb-over techniques with them. The modern C is a better all-rounder and is slightly thinner by about 1.5mm. The modern V is a fairly soft V and really good for thumb-over techniques or if you do lots of bending but it's awkward for shred-style lead where you want your thumb right in the midle of the back of the neck, though from the sound of it I doubt that would be an issue for you. Fender do 50s Strats with the soft-V neck and 60s with the C-neck. You don't get the massive 70s headstock but you should really go for playability over anything else.