Isaiah 7 . 20 says nothing about private parts

20 In that day the Lord will shave with a razor that is hired beyond the River with the king of Assyriathe head and the hair of the feet, and it will sweep away the beard also.

The LORD will bring the king of Assyria upon you: This was bad news to Ahaz, who had been foolishly trusting in Assyria instead of the LORD. It is as if the LORD is saying, “It will seem to you like trusting in Assyria is a clever move, because the armies of Syria and Israel will be defeated. But the Assyrians will end up defeating you also.”

“Thou mightest have remained at home and at ease, and mightest have received the assistance of God; but thou choosest rather to call in the Assyrians. Thou shalt find them to be worse than thine own enemies.” (Calvin)

If Ahaz understood and believed what the LORD said, it would have terrified him. The Assyrians were well known for their sheer cruelty, especially over the nations they conquered. They delighted in the torture and humiliation (shave with a hired razor … the head and the hair of the legs).

To shave off the beard of an Oriental was an unbearable shame to him and was a sign of great sadness and mourning as well as despicable slavery.” We see this principle illustrated by the actions of David in 2 Samuel 10:4-5.