Any time they are out and not enclosed in a really good fence with top, they are at risk. Even in the middle of suburbia you’d be surprised how many predators you have and practically all of them hunt during the day, though your risk is probably greater at night. Some people have no problems letting them roam as you propose, others suffer losses. Safe is a very nebulous term. There is no way for us to determine how high your risk actually is.
I really like a run, even when you let them roam free a lot. It gives you flexibility in managing them. There are times you want to leave them contained. Say you are doing something in the yard that you don’t want them interfering with, they may be at risk. Or you could leave them locked up when you are gone and roaming when you are home until you build your confidence up that they will be OK on their own. Are they going to fly over your fence? You don’t have to have a run but your risk and ability to react to issues are in question without one.
I guess you could get a doggie door. You might be able to train them to use it with the flaps in but maybe just taking those flaps out would be easier. I’d want one that I could lock shut so a raccoon couldn’t open it.
I’m not aware of any blueprints to show you how to build that kind of door. I have one that is just a hinged piece of plywood with a little bracing to stiffen it, but most of mine are guillotine type doors, somewhat like that doggie door but with the grooves the door slides in made of wood. Whichever type you choose, make sure you can securely keep it open as well as closed. You don’t want it accidentally closing and locking your hens away from the nest or food and water.
I guess you’d call it a trick or maybe a technique, but if you screw a frame around your opening to the wood, you have something solid to attach your hardware to. Take maybe some 1x3’s or even 2x4’s and box around your hole to outline it. Put some screws from the plywood or paneling side into those to hold them in place then use those boards to attach your door to. That’s much stronger and usually a lot easier than trying to attach your door to a thin piece of plywood or paneling.
People can always come up with some nice to have’s to add to a coop, but I think you have the basic needs covered.