Can I use store-bought sour mix?

Not if you want the cocktail to be good. Bottled sour mix is high-fructose corn syrup, citric acid, and yellow food coloring — it lacks the aromatic complexity of fresh lemon plus fresh syrup and produces flat, candy-like drinks.

Sour mix in a bottle (Mr & Mrs T, Finest Call, generic well brands) is industrial-grade citrus simulation: HFCS or sucrose, citric acid for tartness, FD&C Yellow #5 for color, sometimes added 'natural flavor' from non-citrus sources, and preservatives. The result is shelf-stable, cheap to use behind a bar, and noticeably worse than a 30-second fresh-squeeze. A Whiskey Sour with bottled sour mix tastes like sweetened lemonade with whiskey in it; the same drink with fresh lemon juice and fresh simple syrup tastes like a layered cocktail with citrus brightness, sugar balance, and visible whiskey character. Bars that use sour mix universally are not paying attention to cocktail quality; the time it takes to squeeze a lemon is shorter than the time it takes to argue with a guest about the drink they ordered. The 'sour' name comes from the basic template: spirit + citrus + sugar, shaken. The mix bottled under that name is unrelated to the historical recipe except in marketing. Use 0.75 oz fresh lemon juice + 0.5 oz simple syrup as the canonical sour spec; sub from there.