Depending on the way the unit is constructed. You might be able to re run the water pipes in heated space. Outside walls are never the best.

Usually though if good insulation is behind the pipes. Plus low air movement is present you can get by in outside walls.

Another thing I forgot to mention although I have never used them. If I were contemplating a heat tape fix. I would jump to the next option. You solder a fitting in the copper line and the heat element wire slides inside the pipe. This theoretically should be the cheapest to run depending on the cost. I have seen them but never used them.

If you were able to place say a twenty gallon water heater inside the apartment then you would have only one water feeder pipe to protect. This suggestion is kind of a quantum leap without knowing what you have exactly. Major changes to systems go from very easily done to virtually impossible or impractical.