I think no matter what you plant, you will have walking dogs running through the space between the sidewalk and the fence and "doing their stuff" as well as wind-blown trash become trapped against the fence.
My feeling is that a hedge would be difficult to clean/pick up such junk from underneath and between it and the fence (unless maybe it is very thick to block intrusion, but thats not likely in the limited sun situation)
Also, if you think about it, when it snows, it will be difficult to differentiate between the sidewalk - the bed - fence and whatever is growing there would be easily damaged by the snow shovel or snow blower....
You might be better off with a mulched bed with annuals and late spring or summer bulbs that will not grow until snowfall is over, and bare mulched bed during the winter. Perennials would have to be late emerging, tough and resilient in case of snow shovel scalping.
...oh, and if you use salt in case of ice, anything planted need to be salt tolerant.
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