Yeah you guys are right I misinterpreted. Sorry about that. Please keep in mind that what I'm writing here is not meant to be negative or poo-poo the idea, I'm just stating the technical facts as I understand them. Okay, so running the evaporator as a heat exchanger inside the cooler itself, would it be safe? Short answer is no, I think it would not be safe even still. I think Lemons tech guys would reject it just because you have pressurized gas, inside some homemade rig you put together yourself, right there in the passenger compartment.
So why is it not safe? Let's walk through it. The evaporator is located under the dash inside that big plastic evaporator/heater core/fan assembly. Let's assume we get rid of all that hardware, except for the evaporator itself, and the two refrigerant lines running to the engine compartment. (Keep in mind I'm talking about the refrigerant lines running to the engine compartment, not the water lines running to and from the cool shirt itself.) The evaporator is most certainly too close the firewall for us to fit the cool shirt cooler around it, so we need to move the evaporator from its original location to where the cool shirt cooler is located (probably the passenger seat area). This means we have to move the evaporator about two feet or so. The existing refrigerant lines are not going to stretch that far (on most cars they are completely hard lines anyway), so we must modify or replace those lines with something custom made. This is the dangerous part.
If we cobble something together from the hardware store or autozone, it is just not going to work. Any material that isn't specifically designed for a/c is going to degrade from the thermal, mechanical, and chemical effects placed on it by the refrigerant. Now you could use something like Tygon tubing, and it would hold, but here's the thing: it would only hold for a short time. Eventually the Tygon tubing will degrade and then one day, most likely right after a pressure increase, it will burst. Even if it's on the other side of the passenger compartment, it's still going to burst pretty much explosively or at least hiss violently, scaring the pissie out of any driver in there, and then it will release an odd smokey-cloudy mist that will fog the cockpit, maybe not bad enough to blind the driver completely, but it's going to be real distracting. Even if it's inside a cooler or even a fuel cell type setup, unless it's completely sealed, this stuff will find it's way out and into the cockpit.
For modern cars, the expansion device is going to be located inside the evaporator assembly itself. This means that one of our two homemade lines running from the firewall to our new evaporator location is on the high side of the a/c system. Pressure inside the high side line will vary with environmental conditions, but worst case be ready for 600 psig, and about 275-300 degF of hot, oily, sticky, gas. Tygon tubing, water hose, even fuel hose, none of it will withstand this kind of punishment. It might hold lower pressures, for a short time. But what I'm afraid is this scenario: your lines have degraded, it's hot out, you come in for a penatly (no ram air), and your radiator/condensor fan is busted (no fan air). Your high side pressure will skyrocket, and that's when the line is going to burst.
But how could we make it safer? If you made your refrigerant lines from all refrigerant grade hardware, obtained proper o-rings and seals, and you knew how and had tools to crimp the hoses effectively, and had a rock solid radiator fan, HPCO and PRV, and you ducted everything aggressively (like you would a fuel line running through the cockpit), then you could make it relatively safer. In that case it would be about as safe as you could make it. Another option would be to replace the evaporator entirely with a tube-in-tube heat exchanger with water. But even then, we gotta consider what happens when you get in a wreck, or flip the car. If the lines are compromised in any way at any time, then to me, it's just too much of a liability. I've personally seen what happens when an a/c system blows (we test for that kind of thing) and in the worst of cases, it's not a trivial affair. I mean, you just do not want to be around it when it blows.
Another unforeseen scary thing is acid. If you don't change your desiccant and/or pull a really strong vacuum, the water remaining inside the a/c system will react with the refrigerant to form acids and other nasty chemicals. Would they chemically burn your skin? I don't think so, they're not that stong, but still, acid. At the very least these acids will erode your refrigerant lines, and accelerate the rate at which they will degrade and burst.
Again sorry guys I don't mean this as being against the idea, I love the idea, it's just seriously not the safest thing out there. If you do decide to do it, then PM me (and this is so ironic that I'm writing this) and I will tell you all the things you could do to make it less hazardous.