When a broody hen raises chicks she does not warm up the universe. She provides a warm spot for them to go to when they need to warm up. Broody hens can raise chicks when there is snow on the ground using this technique. The chicks don't care if that warm spot is from a heat plate, heating pad, heat lamp, or something else. All they need is a spot to warm up when they need to warm up. Even when it is that cold people are often surprised by how long the chicks elect to stay in the colder areas.
But they also need a spot cool enough when it warms up. A challenge when raising chicks out of doors is the heat swings. I've seen it go from below freezing to in the 70's Fahrenheit pretty much overnight. My 3' x 6' brooder is in the coop. I use a heat lamp to keep one end warm enough in the coldest conditions. When it warms up they go to the far end to cool off. I put mine in the brooder straight from the incubator. Your 3-week-olds should do fine in your 34 sq ft coop.
How far can 3-week-olds fly? Mine have no problems flying up to a 5' high roost if a broody hen tells them to. I don't worry about them flying into my heat lamp but that's why you should use wire or chain to secure the heat lamp, you are correct that the clamp would be dangerous if you relied on it.
People are quite often surprised at how quickly the chicks don't really need supplemental heat, but at your temperatures and that age I'd want some heat.
I've seen people with a heat lamp at minimum so they have a place to warm up as needed. Why is that a bad idea?
Heat lamps, if used incorrectly, can cause a fire. They do ignite fires in coops, sheds, even people's houses. Other forms of heat can cause fires or electrical shocks too if used improperly. No matter what you do there is going to be a risk involved. In my opinion if you do not rely on that clamp but firmly secure the heat lamp in place with wire or chain you have eliminated the vast majority of risks associated with that heat lamp.
Another risk with the heat lamp and other methods that heat an area. If you use something small and maybe not well ventilated, it is easy to overheat the chicks. Something like a small aquarium comes to mind. If you are using something like that a heat plate or heating pad is likely the best thing for you to use to provide heat. Small incubators like a small aquarium usually don't work really well outside because of the temperature swings. Your horse trough should work OK, it should be big enough.