I've worked at a couple of mom-and-pop businesses. Most of our customers at a couple of the places were people working at or just above minimum wage.
Were our customers to have their income doubled it would be great for the business. More customers with much more disposable income? That sounds fantastic. And in turn the cost of higher wages for the employees is smaller than the reward from a more prosperous customer base. On a $2 cup of coffee for instance, the wage cost is somewhere between $0.15 and $0.50.
A customer making $8/hour would balk at a $3 cup of coffee, but a customer making $16/hour would have no issue with it. Even accounting for a 15% to 25% increase in cost all the way down our supply chain, we would still come out the better for it. As would most businesses.
Even businesses were wages are the majority of the expenses wouldn't be hurt. If the cost of a service is 75% labor wages, and that cost doubles, you need to raise the price of that service by 35%, right? But your lowest income customers have a 100% increase in income. Probably a multi-times increase in disposable income. That's good for business.
The problem with competing with walmart has little to nothing to do with labor and wage costs. It has to do with Walmart's highly optimized supply chain and one-stop-shopping at very low prices. Doubling of wages would have very little impact on the dynamic between Walmart and smaller businesses.
Though smaller businesses may benefit from a consumer base with more disposable income having to be less price conscious and not having to shop at walmart out of economic necessity.