One can understand that Sandhyavandanam must be done within certain time, and it can be done even before taking a bath. What is the procedure or method to perform Sandhyavandanam without taking bath? What are the details that one must be aware of?

Sandhyavandanam is associated with time. It must be done at the stipulated time. As far as possible, one must take bath and perform Sandhyavandanam. When one is down with a fever or illness, Sandhyavandanam can be performed without taking bath.
Those who are physically unable to take bath, can wash their face, adorn Thiruman, do mantra snanam and perform Sandhyavandanam.
If one is not physically afflicted and is physically sound, one must take bath before performing Sandhyavandanam. It is the practice of the elders.