IMO you should take a complete break from all exercises that cause pain. Substitute in other exercises until the pain's gone.
Once the wrist is ok, stick with DB or machine presses that hit about the same area of chest, without causing the wrist strain. Use different grips in each case to find those that don't cause pain. There's no reason to persist with problem exercises, and BB bench is one of the biggest causes of injuries out there. Often the injuries caused by certain exercises are chronic and won't disappear over time, the problems are a combo of the bar forcing a rigid ROM and the mechanics of the motion.
Also i would suggest keeping the reps moderate at the lowest, as heavy weight with low reps puts more strain on the joints and connective tissues.
Lastly, ensure thorough warmups, take 3-5 minutes.
