C makes the most sense.

B, D, and E all seem to link drivers and telephones. We want to link telephones and usage.

A has modifier problem.
Unlike the use of headset telephones, .......... ,drivers
is wrong
we need to have telephones after ,


in B
besides is wrong
IMO beside is used for continuation.
and here we need some contrast word... we are talking a reverse path from what is allowed to what is not

D
Other than the use of headset telephones, .... , drivers
again modifier problem
after , we need some use of.....


E
Aside from
I have not much heard of in context to gmat
also I think it is not allowing me to take a reverse path


One observation:
Option A B D E must have "," at the end otherwise answer C IMO will not make send

It will become
Unless headset telephones, which allow drivers to keep their hands on the wheel, are used, all drivers are prohibited from using portable phones while driving.

only C correctly expresses contradict meaning in this sentence.