The water at 100 feet would be compressed by the 100 feet of water above the sunken boat by a factor of 0.0361396 PSI per inch of water. Changing from feet to inches and multiplying by the factor gives 43.4 psi at the 100 foot depth. Water from outside the sunken ship would continue to flow into the boat compressing the air in the trapped pocket until the inside pressure balanced the pressure outside the hull. When the water stopped flowing into the hull the pressures inside, outside, and in the air pocket were all equalized at 43.4 PSI (just a shade over three atmospheres). Water is just about incompressible (about 1% per 1000psi) so the factor used is valid to at least 2300 feet.
This cook was an incredibly lucky fellow, he remembered his wife's text message of the Psalm...it was enough to save his life. Do you think he'll ever set foot on a boat again?
PS Many brave men lie asleep in the deep...