This is silly. Don’t do this.
First, Labor Day is a cultural holiday. People don’t celebrate Labor Day in some kind of solidarity with workers. It’s a time to have a day off (if you’re lucky) and get together with friends and family for a cookout.
Also keep in mind that if a business closes, anti-worker right-wingers don’t necessarily have the option to break into the business to work in protest.
Most importantly, being critical of something because you feel that there is a better way doesn’t mean you can’t take part in the ubiquitous thing as it is right now. Capitalists who have yet to explore the concepts of logic will sometimes make – with a smug face – an argument that goes something like this: “You say that you hate capitalism, but I see that you have a smartphone! Hypocrite.” There is nothing further from hypocrisy here, and it just makes the capitalist appear drunk or uneducated.
I am very pro-union (and work for a union organization). But I know for a fact that there is at least one person here who is anti-union. Making a living (selling your labor) to feed your family by working for an organization that you are ideologically opposed to is not unusual. It’s also not as problematic as you sense that it is.