Probably not much help but the Jenn-Air W11231243 is a compatible handle-kit and you can view and zoom in on the screws that come with that handle. There are other handles in the Accessories section of the refrigerator website.

It would appear that the screws would have to just be long enough to screw through the 3/4"-thick door and firmly into an appliance handle (not cabinet handle). This Amerock appliance pull uses a #10-24 machine screw.

An M4 machine screw is likely to be stronger than you in tensile strength, and certainly stronger than the refrigerator seal. However, the force exerted on it could over time pull it into the wood panel unless the wood is very dense. I would certainly use a large washer between it and the panel. Resistance to being whacked from the side and bent could be an issue in some circumstances, and I would be more comfortable with an M6 handle mount for long handles that can resist bumping by using sufficient mounting torque.

I'm forced to admit, however, that the SubZero 3/4 handles' installation guide shows mounting via 10-24 screws, which are 4.8 mm in diameter. So maybe M5 would be sufficiently better than M4.

I don't recall the screw size used to mount the long 1-inch diameter handles I have on my side-by-side 4-foot wide SZ 632.