The gelatinous ooze deal acid damage without saving throws. So if he touch the the gelatinous ooze in any way, he takes damage. He has only 1 HP. Yes, DnD allows shoes to be used as armour, but this is acid damage either 10HP instant or 3D6 unaffected by armour. The only saving throw is at 12 Dexterity, but that's the saving throw to avoid being engulfed, not if you go out of your way to get in the same location. Another saving throw is matched against 12 Strength to get out after being engulfed, but the damage is applied upon each attempt.
How many bloody chapters are we still going to have until this fight is over? Let me guess, the MC will just sit on his hands until the shapeshifter wakes up, and then the fight will resume once more.