Well, if the lake doesn't have a fast refill via the edge, how about simply draining it to the edge. Dig down a couple of Z levels below the lake and then tunnel to the edge, smooth and carve a fortification. And since you want to be able to refill it again later, build a drawbridge there to act as a floodgate. It's about as fast as going for the cavern, but safer since you won't have to deal with any guests down there.
Side view
~~~~~~~~~~ Water in lake
############ Ground under lake.
######X##### Up/Down stairwell.
######X_____ Access tunnel.
######X##### Safety buffer.
______X##### Drain to edge of map.
When draining large amounts of water, I've rarely seen anything above 1/7 water on the Z level above the drain level. Having it 2 Z levels below your access level will let your dwarves keep their feet nice and dry. And given the Z level difference, the draining will go fast. However, the way pressure and flow work in DF, your speed will vary dramatically depending upon how deep the water is. Water that's 2 or more Z levels high will drain RAPIDLY down to 1 Z level. That's due to the pressure mechanics. But once it drops down to 1 Z level, flow mechanics take over. And that is slow. And as long as you're doing the drain project, if you think you might want some waterwheels in the future, you may want to energize some areas where you want future water wheels. You can have 7/7 water sitting stationary in a pool with a waterwheel above it spinning merrily. Trick is that if water has flowed over a tile and then vanishes off the map, that tile is marked as 'flowing' and if in the future, you put water in that tile again, the water is also marked as flowing even if it's not moving at all.