I'm not aware of any mod like you're asking.
I've had no problem with sims buying makeovers. Naturally the business must be open, but the chair must have an assigned stylist also. I've successfully run 3 chairs with one stylist, but 2 is easier, and 1 easiest of all. Each chair can have 2, maybe 3 sims "browsing" deciding to buy a makeover. If no one is browsing at a chair, click on it, assign stylist and leave your sim there long enough to get a couple sims browsing. Then start to do your sales pitches to speed up the buy decision. Be careful because if one decides to buy and then you do a sales pitch, the process starts all over. If you offer a makeover to a sim, make sure you have a stylist assigned to the chair so the buy decision process starts, that is, offer a makeover, then assign a stylist. Going down a row of 2 or 3 chairs works the same, but then you have to keep an eye on what chair has someone that decided to buy and is waiting their turn.
There is a employee massage controller at
www.simwardrove.com that works nicely with a salon. The employee assigned to give massages will approach customers and offer. If the sim was in the process of deciding on a makeover, that process is put on hold until after the massage, then resumes without loss on the meter.
As the business grows, if you have more customers than you have things for them to browse, they are more likely to disrupt sales by social interactions and be engaged in interactions when browsing slots are available. A level 2 business with a max of 4 customers and only one chair means 2 customers are just hanging out and are potential problems for business. 2 chairs will keep them engaged with your business. Don't be afraid to tell customers that have had makeovers or that express no interest in one goodbye.