Can I change the gradient/slope of asphalt walkway with cold patch?
You can certainly fill with cold patch, though for good adhesion you would need to start with getting the area really dry, which will be considerable work as it's a low spot that holds a puddle. What may happen, and is more likely if you don't get it well-dried out before applying the cold patch, would be water getting or staying between the patch and the old asphalt, causing the patch to pop loose when that water freezes.

Both the appearance and the odds of having it pop loose could be helped by sealing the whole area after patching to fix the grade, thus giving a more uniform color and also reducing water ingress.

There's no argument that ripping up and replacing with new hot asphalt or concrete would be less likely to fail long-term, and probably look better, but there's also no argument that it's going to cost a lot more and / or get out of your DIY comfort zone, depending where your comfort zone is.

A third alternative (since you are getting out the cold patch anyway) would be to cut a channel from the lowest part of the low spot to the sump, place a drain pipe in it, and then cold-patch the channel.