If you want to use the classic 1:50,000 Ordnance Survey Landranger there are five sheets which cover the whole route. The route of the Cumbria Way is clearly marked on these maps so it's pretty easy to follow (although we'd argue that it's easier still on the Explorer maps).
However you don't need all of them. At the southern end for stage one (Ulverston to Coniston) you can choose between sheet 96 and 97, both of which cover your day.
As an alternative to the Ordnance Survey you could look at the Harvey map of the Cumbria Way. It's a single strip map of the entire route at a scale of 1:40,000.
Harvey maps are specifically designed for walkers and are made of polyethylene, not paper. These maps are tough, durable and 100% waterproof. They are also compact - not the great bulky package you get with a laminated map - and light to carry.
Be warned that they can be a bit of a culture shock if you're used to reading Ordnance Survey maps as they differ in some ways in the way they mark things up but you soon get used to it.