Hi Jennie,
我不会说中文 is the not the only correct way to say "I cannot speak Chinese," but it is the most used way. The reason is that 会 in Chinese means "to know how to" (as in to know a skill rather than just know information). This does mean you can technically omit the 说 if you want, but 我不会中文 means you don't know how to do anything in Chinese (including write, read, and understand it).
The other examples you've provided have their own meanings (notice the characters I added where applicable):
我不要说中文 = I don't want to speak Chinese.
我不知道怎么样说中文 = I don't know how to speak Chinese (while this means the same thing, it's much longer to say and is not preferred)
我不知道中文 = I don't know Chinese, but since you're using 知道 instead of 会, you really mean you don't know any information about Chinese (which is already awkward to say/hear).
我不能说中文 = I cannot speak Chinese, but this one comes across as though you don't have permission to speak it rather than you don't have the ability to speak it.
我不可以说中文 = I may not speak Chinese. This one definitely means you don't have permission to speak it.
I hope my answers help. Please let me know if you have any more questions =)