A think a basic term for this is "exam proctor" (AmE).
In the United States and some other countries, the word "proctor" is frequently used to describe someone who oversees an examination (i.e. a supervisor or invigilator) or dormitory.
In the United States and some other countries, a proctor can be any teacher or other staff member at a university, secondary school or even elementary school when they are supervising the administration of a test or examination; i.e. the role referred to as an "invigilator" in British, Canadian, Australian and South African English.
An exam invigilator, exam proctor or exam supervisor is someone who is appointed by the examination board and services for maintaining the proper conduct of a particular examination in accordance with the exam regulations. It is the duty of the exam invigilator to watch the examination candidates to prevent cheating during the examination. They are required to ensure that all the exams are carried out according to the rules set out by the exam board which allows each candidate to sit for the examination under equal conditions as other candidates throughout the country.
You can easily explain your specific duties in the CV, particularly if you want to clarify that you travel to schools in the vicinity. If you really want to specify that point in the title, perhaps traveling exam proctor, or maybe visiting exam proctor. I don't know that these are commonly used titles, but I think they make sense.
[Too long to put in the comments/side note]
By the way, you give/administer/oversee/proctor the exam (AmE). The students take the exam. I assume this is what you meant (not take = deliver).
Students can also sit an exam (Cambridge Dictionary). I think this is more common in BrE.
This one is a little tricky for me. Students can also write an exam (Collins Dictionary). I'm not sure exactly where this is common, but I am more familiar with the teacher writing the exam (= producing the exam), not the student writing the exam (= taking the exam).