There are very few OSHA requirements that are different based on the number of employees. Generally speaking, if there is one employee then the regulations apply the same as they do if there are 10 or 300 employees.
In terms of inspection exemptions for smaller employers, there are a few, but they apply only in limited circumstances, generally for small employers who also are in low-hazard industries (or farming) and then only to certain types of inspections. Also, some OSHA targeting inspection programs are based to varying degrees on number of employees. And, OSHA does provide reduced penalties based on number of employees in certain instances.