I'm intrigued, but see a game-balance issue here. The cost of a floating dock capable of fixing a coastal submarine would be about ~250 t as proposed here. Yet a class 0 drydock requires 1.0 infrastructure points, the equivalent of 10,000 t of warship material. That's a real disparity.
If we were to go ahead with this idea, I'd rather consider the floating dock to be a less capable version of a drydock, built with infrastructure materials rather than warship materials.
As for cost, half that of drydock of the same size? And I'd say it was repairs only, no refits or other changes to the ship. Thing is, I can't think of why this would be the case in real life...