Is there any danger associated with rebuilding atomizers and using them? I don't want any explosions...
If you have the proper device, not at all. Almost all electronic/regulated mods will prevent an atomizer that has a short or too low of resistance from firing. This is a slightly different story when it comes to mechanical mods, however. With a mechanical mod, you need to make sure that the resistance of the coil you're building is within the amp limit of the battery you are using as well as making sure that your new coil does not have a short.
Using that Ohm's Law Calculator is key. Simply put two values in there and see what the other two come out to be:
For VV/VW devices, put either the Voltage/Wattage you like to vape at and the resistance of the coil you want. The calculator will tell you how many amps your battery will need to fire the coil. Most batteries will show in their description what their amp limit is - if not, it's an easy google solution.
If you're using a mechanical mod, put in the voltage of your battery (typically 3.7 or 4.2) and the amperage limit of the battery. The calculator will then tell you the lowest possible resistance you can have for a coil.
I understand your concern with an explosion. I was the same way. Just understand this: Most explosions from e-cigs (which there are only a handful of reported cases) are from poorly designed mechanical mods. These mechanical mods are fired with a short and the battery in them ruptures. When this happens, a gas is released from the battery. These poorly designed mods do not have ventilation which causes the gas to build up inside the metal tube creating a type of pipe bomb. Most standard mechanical mods in present day will have ventilation holes to prevent this from occurring.
When building coils, it is always a good idea (if not required) to have a resistance tester on hand to know what you've built. Personally, until I can get an independant one, I just put the coil on my MPV 2 and test the resistance with a built in function. I've had no problems thus far with this method.