Unless they are already a carpet cleaner with their own van, equipment, chemicals, insurance etc and you are effectively subbing work to them they cannot be classed as self employed and any " self employed contract " they sign would be irrelevant to HMRC.
HMRC will always look to you to pay the tax and NI owed by you and them if you are caught treating an employee as self employed when they clearly are not.
The DSS will only be interested in what you paid them, not what you consider to be their employment status.
The only way is to directly employ them whether on zero hours is up to you.
If you need guidance speak to HMRC, who are very helpfull.