I didn't know you were allergic. Wetting it down makes the job smellier and messier, but if you have to do it for the sake of your health, then you have to do it. I always dig it out dry to use as compost or manure top-up in the compost bin. But it doesn't give me breathing trouble.
What I think has worked for me, is our chookhouse is basically a giant compost heap in itself, open underneath to the ground. Earthworms can get in and do their work. The sides are several courses of loose-laid bricks, with a timber frame sitting over the lot. Timber frame has walls, wire and fibreglass sheeting, and a roof of corrugated sheeting. We then got fallen logs from trees about arm thickness and use those for perches. Under the perches we put some wooden boxes and these collect droppings overnight (that's the concentrated manure). I let the neighbours know that there is free manure here, they come to dig it out for themselves and they STILL offer to pay me! I ask them to pay me in grass clippings, which we toss into the chookhouse. The compost/clippings/manure heap fills to the top of the brickwork and the chooks scratch around in the top of that. We keep it dry (keep out the rain) and if it gets wet or smells, I toss in some garden lime and dig it in. We let the chooks out every afternoon and they put themselves back to bed at dusk. Inside, we have 4 litre plastic ice cream buckets as water containers, these are sitting in a wooden box which is now buried (partly) in compost. The buckets lift out for cleaning and are rinsed and refilled every day. The feed hopper sits on two more boxes (straddles them) so chooks can creep underneath to lay eggs in privacy if they choose. We have built brick steps to get in and out, because some of the older hens struggle with the door being several course of bricks high. The steps are easier for us to get in and out, easier than a ramp (which I had originally planned).
I can skip digging this out literally for years. Eventually the pressure builds up on the bricks and they fall out. Then we dig out enough (it is now pure, clean, perfect compost, no smell even when wet) so there is no pressure on the bricks, and then rebuild the brick wall. Only a few minutes' work.
When we need a lot of compost, we turf the chooks out for the afternoon, knock down some bricks, dig out as much as we have the energy for and barrow it to where we want. Then put in the call for grass clippings to refill the brick pit!
The chooks eat grass clippings (as much as they can) and the rest composts. This also keeps them a bit warmer in winter. I can throw the worst weeds in there, and what doesn't get eaten breaks down. Any weed trying to grow, gets eaten. And the eggs are marvellous!
Our four new hens are fitting in happily. They still look awful, feathers sticking out at all angles and bare patches everywhere, but given time they will fill out again. They can't believe their luck - I see them dust-bathing (yes, the stuff in there is dry enough in places for them to dust-bath) and scratching around. They have never had the chance to do anything like this, they were living in wire cages until Monday.
If digging this out is a problem for you, find a neighbour who doesn't have allergy issues and who can be paid in manure.
Marg