That would be quite a hack. Most of the Home Depot tubing is quite large. Perhaps thermostat tubing scrounged out of something? I know I've seen coils of small tubing, I think. Maybe refrigerators? Or, Washing Machines?

Is your cable stainless or galvanized? I've found it more difficult to solder stainless cable than galvanized.

Anyway, I'd just hunt down the cables you need. Most department stores will sell cable kits, albeit cheap kits. Keep what you need and toss the rest. I haven't checked bike shops, but I thought some were open.

If you hunt, you can also find thin bulk cable. You may be able to solder on a solid end to the cable. I think I've seen some Youtube videos.