FUT (strip surgery) can be done unshaven. There are a few options for FUE;
Recipient unshaven FUE: The donor area is shaven only.
Limited shaven FUE: Strips are shaven at the donor area so that the overlying hair camouflages the shaven areas. The graft number is limited in this method.
Unshaven FUE: Attempts at doing graft extractions without shaving cause a significant increase in the transection rate and graft damage. It should only be done by experts and the graft number should be limited.