If I hire an unbonded home handyman, will a letter signed by him stating that he will not sue me if he gets hurt protect me from a lawsuit.

Perhaps.  A written waiver of future claims is not favored by the courts, but if written clearly it may be enforced to prevent future claims.  You would really need to examine the language used to be certain that it is written broadly to cover all possible future injuries, claims and damages. Such a waiver will not prevent the filing of a lawsuit, but it may provide evidence that could be used to have the case dismissed at an early stage.  You need to consult with a lawyer regarding this issue.