It is merely the 'device' used to execute our Lord. An argument often made that he would not have been executed using a 'pagan' cross is not relevant as the execution 'device' is not relevant.
On the other hand if one is arguing from an interpretation point of view you will note that Cross/Stake/Pole/Tree is used and while it could be argued that it should be interpreted more correctly as being one of those, as all scripture is inspired by our Heavenly Father and should be correct and consistent, it would seem that Cross/Stake/Pole/Tree is used almost 50/50 from my research.
I agree that should not be the case as either it should be one or the other, but I have yet to find conclusive scriptural, not historical, proof which actually points more likely to evidence for either.
Also, it’s not a talisman or special or to be worn as a Christian symbol IMHO. Imagine wearing the gun that killed your husband or relative around your neck in remembrance of their sacrifice so that you could be freed from a hostage situation. You would not!