Please, help. I want to study in China as a exchange student

Please, help. I want to study in China as a exchange student, but I don't have a HSK grade.
Hi, I'm a student from other country who studies Chinese history.
It has been one of my dreams to go China as a exchange student to study my major.(after all, I'm a Chinese history majoring student :-))
So I will apply for Chinese schools through my schools' exchange program this summer.
As I don't have HSK grade, I can only apply for schools which don't require HSK grade.(And even if I take the HSK test right now, the result won't come out in time, so I won't be able to submit the HSK grade to school in China anyways..)
But there is the problem.
Even if the school don't require HSK grade for 'applying', some school have language requirements for study regular courses.
In that case, only classes I can take in there will be the classes exclusively prepared for exchange students;basic Chinese language courses
(And my school only warned about this problem, not giving any further specific informations about these schools.)
But I want to study at least one Chinese Culture related course(Which is a regular course).. so I'm posting my question here for you guys' help..
These are the lists of schools which I can apply.
(My university is twinned with those universities)
1. 遼宁大学校 Liaoning University
2. 上海外大 Shanghai International Studies University
3. 吉林大学 Jilin University
4. 中国人民大学 Renmin University
5. 浙江大学 Zhejiang University
Please let me know if there is schools which needs HSK grade to study regular courses; It has to be super clear..
(I'm asking the language requirement which applys for the exchange students. Oh and I'm an undergraduate student.)
Thank you.

You can have a try in “Tianjin EZ-Language Institute”,
the teachers there are rich in experience. I studied the HSK5 for only two
months, and passed the examination successfully. If you follow the teacher’s requirements
and suggestions, you will pass most examinations smoothly! And I compared thetuition with other schools, EZ is cheap!