I used to live by the canal there. You wouldn't call it particularly narrow - usual canal scale, between 11 and 13m wide. Yes, you can fish the canal with a 4m whip. It's one of the simplest, cheapest ways to get started, and you can catch fish with it, but you'll find it quite limiting.
You can rig up with a little float and fish your side of the canal. But this canal, below the huge set of locks at Northgate, will rarely be still once boats start moving, and the canal will flow quite hard as the locks open. You'll find it hard to keep your float still or under control any more than 4m out, and you'll have about 3m of line above your float making that a bit harder. If you walk along and find some anglers, you'll see they mostly use poles with a short line to the float and break them down to land fish, re-bait etc.
If you accept the 4m whip is rather restrictive, you can still get some success with it by concentrating on a spot where you can hold your float and bait still. Sit facing a bit downstream ie away from Chester. find the depth 4m out with a plummet and set your float a couple of inches deeper. Find the spot down from you where your float will stop drifting and settle around 4m out. Fish there and feed a few maggots every few minutes a couple of feet above your float so they end up on the bottom where your bait is. You can catch plenty of fish just down from the end of your rod/whip, provided you don't scare them, feed them a bit and present them with a still bait that's not being moved around randomly by the wind or the flow dragging your float along.
Have you tried the new basin below the old horsebridge at the Whipcord Lane basin? There's no effect from the locks there, and it easier to get your float working properly to begin with.