There is no danger with asbestos unless you physically damage it in such a way as to spread the spores around. Asbestos contained within materials such as caulking, plaster lathe, floor tiles, and electrical cords is of low risk. It's only a danger when you are doing home renovation, and have asbestos containing insulation in your attic or any other materials in the home that are going to be torn down and spread dust and debris. Vermiculite attic insulation for one example is one of the most dangerous types of asbestos you could have in your house, as it is very easily spread by disturbance and since the spores are free-floating within the material.
Asbestos is designed to be heat-proof so if being used in motor wiring, the wires will be just fine because that is its job. However do inspect the wiring for any visible fraying or damage. They would not have used asbestos in cloth vacuum bags or on the hose liner, I believe those bags were made out of corduroy or some other such material, and the hose from a cotton type.
I have several vacuums with asbestos cords on them (will need to be replaced due to general age decay) and I have asbestos wrap on my HVAC duct joints, and its perfectly safe. When I go to replace the vacuum cords, just a simple paper mask will be fine because it is very difficult to release any spores from the wrapped cord, unless you were to take a belt sander to it and start sanding away at it.
