Hi PMB
If you are starting from Workington then you won't be going over Whinlatter (shame as the view and ice-cream van at the top are good), although that doesn't mean that the route is flat.
There is a track round the bottom of Ling fell which joins the Whitehaven route at Branthwaite, although the Sustrans map warns of a steep rough decent on part of it. I haven't been that way myself.
Another option for getting to Keswick is to go around the North and East of Bassenthwaite Lake by going through Dubwath, up the B5291 to Kilnhill and along the A591 back to Keswick. The A591 is significantly quieter than the A66 but does mean you have to cross the A66 at the roundabout outside of Keswick.
From what I have ridden (up to Keswick) and driven past (as far as Penrith) I don't remember there being any significant sections where you have to ride on the A66. On the few occasions there are no alternatives I think there's an off-road path at the side of the road.
Where are you intending staying by the way? Penrith is quite a long way for a 4 day ride, I'd be looking more at riding to Keswick or Threlkeld on Day 1. There's very little climbing past Stanhope (in fact it is pretty much downhill) so you can afford to have longer finishing days instead of trying to pile lots into the more undulating western section.