Homeowners with access to their furnace's manual and a bit of experience with wires should be able to replace heater wires without calling an expert, but it's important to exercise proper safety precautions. Disconnecting the power and discharging capacitors is important for preventing injuries. When in doubt, call a professional.
Furnace wires are designed to withstand regular use, but furnaces are often placed in basements and other areas where the temperature can vary dramatically and dust can accumulate, which can cause the insulation on wiring to wear down over time. Operation manuals typically note the location of capacitors and have instructions for discharging them, but it may be wise to invest in a no-contact voltage and current detector to make sure the system is completely disconnected before touching any wires.