Those who go out for work, when they return home after work, must they take a head bath before evening Sandhyavandanam, or will the prokshana mantras of Sandhyavandanam will purify them? Since Ashtakshara mantra is involved, had this doubt.

It is proper to perform austerities such as Sandhyavandanam with physical purity.
If possible, take a head bath before Sandhyavandanam.
If not possible, without taking a head bath, one can take kanta snanam (That is, taking bath up to the neck and washing the face. Even if this is not possible, one can wash the face and wear fresh Thiruman and perform Sandhyavandanam after doing mantra snanam).
These matters are related to one’s physical capability or incapabilities.