I don't know about employing someone, here, who works abroad.
AHV (Social security)
To employ someone in Switzerland, the employer must register that person with the AHV (social security office). For the employer to be able to do that, the employee must already be living in Switzerland with a valid permit, or be Swiss.
The employer must declare to the AHV office the anticipated salary over the next period. You'd have to check in your Canton what that is; typically for one quarter, for six months or for the whole year. Then, the AHV sends the employer a bill for the corresponding contributions, which the employer must pay in advance. The employer pays, to the AHV, the employer's and the employee's contributions, i.e. 50% each.
Each month, the employer deducts, from the employee's salary, the 50% due by the employee. This must be clearly declared on the salary slip.
At the end of a year or so, the AHV asks the employer about the actual amount paid, and tallies up, charging more if needed or giving a refund for overpayments.
AHV office in Bern:
https://www.bern.ch/politik-und-verw...-zweigstelle-1
Accident insurance
The employer must also buy accident insurance for the employee. If the employee works, on average, less than 8 hours per week, then the employer must buy only the obligatory BU (Berufsunfallversicherung) which covers the employee for the costs of accidents at work and also on the direct, uninterrupted journey between work and home. If the employee works, on average, 8 hours or more per week, then the employer must also buy NBU, which includes BU, but also covers the employee during all their free-time. It is irrelevant if the employee already has such cover through some other employer; it is still obligatory. The costs of the NBU can be passed on to the employee, and deducted from their salary. Some employers do this, others just bear these costs themselves.
This kind of insurance can be bought from many insurance companies, and it can be good to tack this on to any other insurance the organisation already may have.
Vacation
Vacation pay must be declared in the contract, and specified separately in the salary slip.
Four weeks is the usual amount, of which at least two weeks must be taken at once.
Salary or hourly wage?
For small percentage jobs, as this would be, and depending on the level of remuneration and the consistency of the workload, it might be easier to pay an hourly wage rather than a salary. Then, of course, it become essential to have a proper recording system (time-sheet).
Even staff working on an hourly basis have a right to paid vacation. Then, though it is common to pay that surcharge out to them, together with each hour's wage. However, it is law to declare that, separately (see above).