A "no trespassing sign" doesn't cary any force on its own. Were there no laws against trespassing on private property, then yes, you'd have a point. Whether someone has a sign or not, the law is the same, and if the police show up and then point their guns at you (whether real or metaphorical), it's more or less the same situation.
You have a choice in the case of the gun toting property owner as well. The choice is to leave, or be risk being shot and killed. As you say, not all choices are between equally desirable outcomes...
A "no trespassing sign" doesn't cary any force on its own.
It conveys the property owner's intent regardless of whether there are any laws to back it up. If you choose to disregard the owner's intent, you are disregarding his property rights, whether or not the law makes that illegal. Using signs, fences, and other boundary markers to delimit property is logically prior to any laws about property rights, and those boundary markers can succeed in defining property rights even if there are no laws to enforce them.
If you know your neighbor doesn't want you to walk on his lawn, and has a sign up conveying that intent, is the law the only thing that can keep you from disregarding his intent? If you know that the goods inside the corner grocery store, whose owner is known and respected by everyone in town, aren't yours, and you find the door unlocked, is the law the only thing that keeps you from going in and looting the place?
People can have other reasons besides laws for defining and respecting property rights. It's easy to forget that now because our system of property rights has been evolving for thousands of years. But that doesn't change the fundamental game theory involved. The fact that many people now think that the law is the only thing that keeps them from violating others' property rights is a bug, not a feature.
You have a choice in the case of the gun toting property owner as well. The choice is to leave, or be risk being shot and killed. As you say, not all choices are between equally desirable outcomes...