Sorry for the late reply and here is the answer to your question.
There is nothing at all to indicate wireless headphones would pose any issues just because they are wireless. The real problem has always been the use of equipment that has features which specifically alter, enhance, boost, or adjust the quality of the sounds in any way such as surround sound, EQ, bass boost, etc. You should have no problem with wireless headphones.
I would suggest that you try it with both types (wired and wireless) and see if you notice any benefits one way or the other and then post your findings here.
So to sum up, you should not have any negative effects by using wireless headphones. I hope this helps to answer your question.
Have a great week!