It is perfectly possible to do an unshaven FUT (FUSS, strip surgery). In fact, it is even possible to use a technique called 'long hair transplant'. This is the same procedure done while preparing the grafts with long hairs on them, so the procedure is not only unshaven, but also the grafts add...
A great first step would be an online consultation. Often you can submit photos to top hair restoration surgeons for a complimentary evaluation and assessment. This should help lead you in the right direction. Having multiple consultations with different doctors will let you know your best options.
