It should be "I wish you all the very best for whatever journey you may embark on after the exam." No one would write or speak like this now. It is just too old-fashioned. Most people would just say,"All the best!" Regarding "embark", the correct usage is "to embark on a journey".

You embark (up)on a journey, but your sentence uses "embark... a journey", which is why it sounds unnatural. "Post the exam" is also a very unnatural time-clause. The "-bark" part of "embark" literally means a small ship. So by using "embark", you are giving the other person a sailing analogy. Keep that in mind when using words like this.