Do you need a wild destruction? Mount a Viking Press on the Shelf:
Let's talk about it for a second. To start with, I always like a thumb-free grip when pushing overhead. It is preferable to use a folding edge grip and tilt presses with your bench. But for the overhead work, I've never seen anyone who did not squeeze as he headed for a stupid grip.
With a dumb-less grip, you get a more neutral hand position and a better alignment with the elbow joint. This tends to reduce the load on the shoulder and reduce the torque on the elbows (as we look at a better distribution of tension across the wrist, elbow, and shoulder when you have alignment through these three joints).
The other factor here is that you use the plate-loaded end of the dumbbell, so it's like using a thick rod to press. Thick bar work is a great option for those who have joint pain while squeezing. The load is distributed over the entire hand and thus distributed more evenly on the flexors and extensors of the forearm.
If you are using a standard sized pole, placing your thumbs around your arm and aligning your wrist with your elbow should not result in elbow, bicep, and forearm pain. This is mostly due to an imbalance between the muscles of the forearm or a bit too short and / or tight in the rotator cuff.
Try the Viking Press with a (mostly) thumb grip and see if you can do it painlessly. If so, it's most likely related to something above. But now you have a way to train it at least painless, so you can go wild again.
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