Are you not required to leave a signed copy at the departure airfield?
Recently retired from freight, but would be std-10 (approx) ACARS weight block arrives allowing ZFW, CG to be entered, TOW agreed, TO performance completed, bugs and derate set. When final load sheet arrives, cross check that figures are correct, sign load sheet and leave signed load sheet and NOTOC with the ground staff.
Often an unsigned load sheet arrives shortly before loading complete allowing the cross checking to be done and providing the final signed load sheet has the same issue number/time stamp it can just be signed.
hth