Professor Hawker begins work in August, just 10 months after starting his last post as deputy chief executive of Westminster City Council, where he was formerly director of children's services.
In a previous job with the Qualifications and Curriculum Authority, he was in charge of testing. But any possibility of Sats being revived in Wales would alarm the profession.
Gruff Hughes, general secretary of UCAC, the Welsh-medium teaching union, said: "That's something we got rid of and we don't want to go back to it.
"Professor Hawker is coming to a different curriculum and has a great deal of learning to do about how things happen."
Mr Hughes' concerns are echoed by Dr Philip Dixon, director of the Association of Teachers and Lecturers Cymru. "We hope he's prepared to learn from what we've done and respect the changes, especially to the testing regime," Dr Dixon said.
Both are keen for Professor Hawker to listen when he takes over the Department for Children, Education, Lifelong Learning and Skills.
Professor Hawker, an Englishman, replaces Australian Steve Marshall, who earlier this year left for a post in Ontario, Canada. The new education chief has described his appointment as "a dream job", although he declined to be interviewed by TES Cymru.
The Assembly government was unable to provide data on how many candidates there were for the job, or how many were Welsh.
The hunt for Mr Marshall's successor began in February and was organised by the Assembly government's executive recruitment partner, Veredus. The salary for the job was advertised as "up to pound;125k", but with more available for an "exceptional candidate".
Shortly before taking up his last job, the new education chief was made a professor for a five-year term by the College of Teachers, with a remit to "spread his expertise internationally". The role entails lecturing, writing and being on panels to admit new fellows to the college.
But the government insists his job in Wales will be full-time. The spokeswoman said: "Part of his role will be to learn from other countries and take part in international debates about improving education, which will be of direct benefit to Wales."
UCAC stressed the need for Professor Hawker to understand Welsh culture. "This is a society where a quarter of children are educated in the medium of Welsh," said Mr Hughes.
"He will have a big learning curve. We're disappointed it was felt there weren't people in Wales of the right calibre for the job."