Jamieson, Fausset and Brown on Job 17:3

3. Lay down now--namely, a pledge or security; that is, be my surety; do Thou attest my innocence, since my friends only mock me (Job 17:2). Both litigating parties had to lay down a sum as security before the trial.

put me in a surety--Provide a surety for me (in the trial) with Thee. A presage of the "surety" (He 7:22), or "one Mediator between God and man" (see on Job 16:21).

strike hands--"who else (save God Himself) could strike hands with me?" that is, be my security (Psa 119:122). The Hebrew strikes the hand of him for whom he goes security (Pr 6:1).