My feeling is probably you are going to have to work through that 'freaking out' stage, being there for him and reassuring but being prepared for some major upset. There isn't really a way to do it without I don't think at this age
- even the 'no cry' author says the same for toddlers. I would as step one get that cot side up, with DH holding his hand. I'd then try introducing a lovey (blankie-type), so DH holds his hand in the lovey so hopefully transferring some of that security feel to the lovey instead of the hand. And then go for something like sitting beside cot but no touch, halfway to door, in doorway, outside doorway. The key is to keep moving forwards - and expect a bit of upset with each new step. He and you can do this
And you all deserve a better sleep!