Just leave the damn thing the way it is. It will work just fine for your use.
If it worries you, buy a nylon rain cover for use during the walk from downtown.
If you're bugging out on foot in an urban area, you've got other problems than camouflage. Mostly just problems of avoidance and interaction with others. In an emergency foot movement, you can either avoid folks, defend what's yours, or outrun pursuers. Otherwise... sooner or later someone is going to be in your face and tell you to give up the bag... regardless of color.
That Woodland pattern will work a lot better in an urban area than a dyed black ruck will work in a vegetated area. Black anything (gear or clothing) is a horrible color in the woods and is a poor choice for most urban areas except when crouched in a very dark shadows (like an alley). Black particularly sucks in daylight, isn't much better at night, and suffers when viewed through night vision devices.
Black blends in while you are in a crowd or riding public transport. Other than that, it doesn't offer any actual visual camouflage. It just offers a deception gambit that may work among folks who are already mostly ignoring you. People who are interested in you (predators, neighborhood watch, gang lookouts, LEO, or military) will dial in on any pack like a rat sniffing cheese... regardless of color.
Those who want to know what's in your pack will focus on the fact that you have a pack... period. Not the color. Everyone else will either completely ignore you or just give you a glance.
Eventually you're going to wind up somewhere with vegetation: a city park, a backyard, a drainage ditch or canal, a grown-in patch of weeds around an industrial park, a copse of scrub or trees, or just in the middle of somebody's landscaping. The Woodland pattern will prove useful. Even in urban terrain.
I have walked across major urban/suburban/industrial terrain wearing Woodland, carrying a pack, and with a rifle to hand. While folks were looking for me. It can be done.
I've also done a fair amount of low profile foot surveillance / counter surveillance work in urban centers. Dressed gray man style.
You can change human perception by use of props, by having an apparent purpose, by seeming to be something...
Woodland pack? Add a plastic hard hat, handheld radio (doesn't even have to work), clip ID badge, work pants, boots, and minimal tool belt. Nobody will question you. Work crew. Obviously you've got work gear in that pack.
Stick a couple of baguettes from the bakery protruding from the top of the pack. Obvious grocery shopper. Not threatening.
Add lightweight neutral external props to your pack. An umbrella, diaper bag, or child's stuffed animal. Slap on a patch or flag: God Bless the USA, University, Save the Whales, Global Warming, Boy Scouts of America, etc. Your pack goes from looking like a war bag for the apocalypse... to just looking like some guy carrying everyday stuff.
Have a puppy on a leash or an empty child carrier strapped to your pack... and no one will ever notice the bag. Have a bunch of knives, machetes, hatchets, bed roll, and magazine pouches attached... and you are gonna attract attention.
