In case somebody is interested, ASU has a nice summary of how to use WeBWorK with the Respondus lockdown browser. It is for canvas, but I tried myself (not with students) and it seem to work in Blackboard too.
https://math.asu.edu/sites/default/files/respondus-monitorwebwork-instructionsk_1.pdf
I think I rather try to monitor students' exam through zoom in person.