What the damages would happen if you did not use Antistatic Wrist Strap?

Possibly nothing. But also possibly destruction of sensitive components. If you're working on something that specifies a wrist strap, why not use one? It's only a few bucks. ----

If you do not understand the work well enough to accomplish it yourself properly and safely, don't try it. Consult a professional electrician, as they are proficient enough to do it properly and safely. When working on electrical circuits and equipment, make sure to de-energize the circuit you will be working on. Then test the circuit with a definitive means to make sure it is off (multimeter with metal tipped leads, voltage tester with metal tipped leads, etc., not a non-contact tester, which is non-definitive.)