By small I was thinking along the lines of between a Swiftsure and Trafalgar as opposed to a Los Angeles for example, with an in service date of around 2010 - would that still pose the same problems you stated?
As for cost it will be expensive - in the real world probably unreasonably so - but I figure I can stretch the truth every now and then.
My main reason for not just going for a Trafalgar (other than time frame) is that then I won't get to draw the submarine myself, and in this AU there is a lot of technical cooperation with a slightly more financially healthy UK so I'd imagine that would help reduce certain costs.
If you're going for UK cooperation, you're going to end up with some kind of Astute. Which BEGAN as a design for a Trafalgar with an updated reactor core. Designing a nuke sub is a very dedicated process, and even the Brits had lost enough expertise that they needed US help to get the Astute program going. Having Recherche in the program might help enough that the first Astute boats will be delivered earlier, and without US help. But they're not going to be designing two completely different boats.
Realistically you're not going to get a boat smaller than a Trafalgar, and if you're going for the Never-refuel PWR-2 reactor (this lessens the industrial base you need) you're basically looking at a boat the size of the Astute. The PWR-2 is not small, and it drives the size of the pressure hull.
Of coure you can decide you don't need the huge sail with the spec ops lockers, which means the hump goes as well, you gain some top speed, and you can change the rudders to an X configuration if you think you need to bottom out/operate more in brown water, but if you're working with the UK, you'll end up with an Astute-lite.
Which admittedly is a very very nice thing to have.