I don't think taking percentage is a good idea. It always leads to problems. I don't think the person can be legally self employed if you are taking a percentage on ongoing bases. I don't know how the rules are in UK but here it depends what Revenue Canada sees is what goes. It doesn't matter what the contract is and what I sign. The more control you have over the person and their business the more this can be employer/employee situation.
If you control the schedule, opening hours, products used, days off and the person works with you on ongoing bases- then you are an employer.
Independent contractor
In reality independent contractor person would do occasional jobs for you. For example: we do manicures, pedicures and brows. I have a wedding to do and I'm servicing 8 people. They all also want lashes. So I hire self employed person (independent contractor) for the day, she brings her tools, she does the job, she gets paid (she invoices me), I pay her, she leaves.
Booth renter
You rent a space inside of your salon for a set amount of money. You are just a landlord now. The person comes and goes as they please, they have the key, they charge the client, they take care of their taxes, ideally they have their phone number, they buy their products and set their prices.
This is a totally seperate business operating inside your location. That's all.
You see, you can't have your cake and eat it too. You can't expect your tentant do your reception and if you think that they should, the lines are too blurred.
If I rent an appartament I have a contract and rules to follow, yes, but the landlord cannot tell me when to come home and what do wear.
You can't have help (in form of reception) but not have any responsibility like you would for an employee.
If you want to have an employee then you have to pay their vacation pay, holiday pay, pay at least minumum wage for all the time they are available for you and all their deductions