Like answering "yes" did in the OP...
If I answer no there needs to be legal grounds to search or I must give permission which isn't happening. In the end I know I am transporting legally but over zealous enforcement can still harm me plenty while the wheels of justice grind me up until I am found innocent or charges dropped.
Personal decision and while I often side with the LEOs they have rarely been on the side of the 2A or COTUS when it comes to these matters. There have been enough well meaning individuals ground up by the system after voluntarily attempting to comply with the shifting laws and enforcement strategies around the 2A that I will never voluntarily give information which can only hurt me.
"Religions are all alike - founded upon fables and mythologies." Thomas Jefferson
"The way to see by faith is to shut the eye of reason." Benjamin Franklin